Prepared in cooperation with the U.S. Environmental Protection Agency

Water-Quality Response to Changes in Phosphorus Loading 

of the Winnebago Pool Lakes, Wisconsin, with Special 

Emphasis on the Effects of Internal Loading in a 

Chain of Shallow Lakes

6

5

nm

X

^

^

^

^ ^

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4

2

3

1

2

3

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Lake Poygan

Lake Butte des Morts

Lake Winneconne

Lake 

Winnebago

Fond du Lac

Oshkosh 

Neenah 

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EXPLANATION

3 Bathymetric contour—Depth in meters

Lake sampling site

Gaging and sampling station

River sampling site

Scientific Investigations Report 2018–5099

U.S. Department of the Interior

U.S. Geological Survey
Cover figure. Winnebago Pool Lakes, Wisconsin, and their watersheds, with sampling locations identified.
Water-Quality Response to Changes in Phosphorus 

Loading of the Winnebago Pool Lakes, Wisconsin, 

with Special Emphasis on the Effects of Internal 

Loading in a Chain of Shallow Lakes

By Dale M. Robertson, Benjamin J. Siebers, Matthew W. Diebel, and Andrew J. Somor

Prepared in cooperation with the U.S. Environmental Protection Agency

Scientific Investigations Report 2018–5099

U.S. Department of the Interior

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

RYAN K. ZINKE, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2018

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as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Robertson, D.M., Siebers, B.J., Diebel, M.W., and Somor, A.J., 2018, Water-quality response to changes in phosphorus loading of the Winnebago Pool Lakes, Wisconsin, with special emphasis on the effects of internal loading 

in a chain of shallow lakes: U.S. Geological Survey Scientific Investigations Report 2018–5099, 58 p., https://doi.

org/10.3133/sir20185099.

ISSN 2328-0328 (online)
iii

Acknowledgments

We would like to acknowledge Keith Marquardt and Kevin Kirsch of the Wisconsin Department 

of Natural Resources (WDNR), and Jean Chruscicki, Dave Werbach, and Alie Muneer of 

the U.S. Environmental Protection Agency (EPA) for their insight on stakeholder needs 

throughout the study. We thank Keith Marquardt and Mark Sesing (retired) of the WDNR for 

help with obtaining water-quality, septic, and point-source data used in this study and their 

helpful comments on the design of the study. We also thank Jean Chruscicki of the EPA and 

Emma Lorenzen of the WDNR for providing comments on earlier drafts of this report.

We would like to acknowledge Paul Reneau, Peter Hughes (retired), Dave Owens, Troy Rutter, 

and Dan Olson (retired) of the U.S. Geological Survey (USGS) for help installing and operating 

the buoy on Lake Winnebago and for assistance collecting and processing river data. We thank 

Jim Kennedy of the USGS for assistance with creating maps for this report. We thank Herb Garn 

(retired) and Mary Anne Evans of the USGS for providing helpful comments on earlier drafts of 

this report.

Funding for this study was provided by the U.S. Environmental Protection Agency as part of 

Great Lakes Restoration Initiative.

v

Contents

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

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

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

Purpose and Scope ..............................................................................................................................4

Methods...........................................................................................................................................................4

Study Area..............................................................................................................................................4

Data Collection......................................................................................................................................4

Lake Water Quality ......................................................................................................................4

Lake Morphometry.......................................................................................................................6

Lake Stage.....................................................................................................................................6

River and Tributary Monitoring and Load Computation.........................................................6

Sediment P Release ....................................................................................................................8

Meteorological Data ...................................................................................................................9

Numerical Watershed and Lake Models ..........................................................................................9

Watershed Model—SWAT.........................................................................................................9

Lake Models..................................................................................................................................9

Mass-Balance Model ........................................................................................................9

BATHTUB Model ...............................................................................................................10

Jensen Model....................................................................................................................10

Lake Water Quality ......................................................................................................................................11

Hydrology and Water Budget ....................................................................................................................17

Changes in Water Level and Lake Volume .....................................................................................17

Surface-Water Inflow and Outflow..................................................................................................18

Groundwater........................................................................................................................................18

Precipitation.........................................................................................................................................18

Evaporation..........................................................................................................................................18

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

Phosphorus Inputs to the Winnebago Pool Lakes .................................................................................23

Nonpoint Surface-Water Inputs.......................................................................................................23

Precipitation.........................................................................................................................................27

Groundwater........................................................................................................................................27

Septic Systems....................................................................................................................................27

Point Sources ......................................................................................................................................27

Upstream Pool Lakes..........................................................................................................................30

Surface-Water Outflow......................................................................................................................30

Release of Phosphorus from Lake Sediments ...............................................................................30

Accuracy of the Phosphorus Budget and Total Sediment P Release........................................32

Summary of the Phosphorus Budgets for the Winnebago Pool Lakes......................................32

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

Water-Quality Modeling with BATHTUB.........................................................................................34

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

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

Response in Water Quality to Basinwide Changes in Phosphorus Loading....................37
vi

Contents—Continued

Potential Water Quality.............................................................................................................40

Effects of Specific Phosphorus Reductions from the Watershed.....................................40

Effects of Internal Loading on In-Lake Water Quality..........................................................41

Water-Quality Modeling with the Jensen Model ..........................................................................43

Algorithms, Data Requirements, and Calibration .................................................................43

Response in Water Quality to Basinwide Changes in Phosphorus Loading....................47

Potential Water Quality.............................................................................................................51

Effects of Specific Phosphorus Reductions..........................................................................51

Importance of Internal Phosphorus Loading ..........................................................................................51

Effects of Changes in Phosphorus Loading Cascading Down a Chain of Lakes...............................52

Summary and Conclusions.........................................................................................................................53

References Cited..........................................................................................................................................54

Figures

1. Map showing the Winnebago Pool Lakes and their watersheds, 

with sampling locations identified .............................................................................................3

2. Graph showing distributions of temperature and dissolved oxygen in 

Lake Winnebago in 2012............................................................................................................12

3. Graphs showing near-surface total phosphorus, chlorophyll a, and 

Secchi depths in the Winnebago Pool Lakes 2009–11.........................................................13

4. Graphs showing summer-average near-surface total phosphorus, 

chlorophyll a, and Secchi depths in Lake Winnebago, Wisconsin, 1976–2015................15

5. Graph showing measured and estimated volume of Lake Winnebago, 

water years 2009–14...................................................................................................................17

6. Map showing monitored and unmonitored areas of the watershed of the 

Winnebago Pool Lakes ..............................................................................................................21

7. Graphs showing total phosphorus concentrations measured in rivers throughout 

the Winnebago Pool watershed and in Lake Winnebago, 2009–11...................................24

8. Graphs showing the average annual and average May–September phosphorus 

inputs into the Winnebago Pool Lakes, by source, water years 2009–11 .........................28

9. Graph showing measured and estimated near-surface total phosphorus 

concentrations in Lake Winnebago, during 2009–14 using the 

mass-balance approach............................................................................................................33

10. Graphs showing measured and simulated (with the BATHTUB model) 

summer-average near-surface total phosphorus concentrations, chlorophyll-a

concentrations, and Secchi depths in the Winnebago Pool Lakes ...................................38

11. Graphs showing simulated changes in summer-average water quality 

in the Winnebago Pool Lakes, in response to various phosphorus-loading 

scenarios (table 12) using the BATHTUB model....................................................................39

12. Graphs showing simulated changes in summer-average water quality 

in the Winnebago Pool Lakes, in response to various phosphorus-loading 

scenarios (table 12), with internal loading reduced by 25 percent using 

the BATHTUB model...................................................................................................................42

13. Graphs showing phosphorus release, sedimentation, and net internal 

phosphorus loading for Lake Winnebago, water years 2009–13, on the basis 

of Lake Winnebago Jensen model results .............................................................................46
vii

14. Graphs showing measured and simulated (with the linked Jensen model) 

near-surface total phosphorus concentrations in the Upper Pool Lakes and 

Lake Winnebago, water years 2009–13 ..................................................................................48

15. Graphs showing simulated annual geometric mean total phosphorus 

concentrations for the Upper Pool Lakes and Lake Winnebago, during 

water years 2009–2145 after a 75-percent reduction in external phosphorus 

loading using the linked Jensen model...................................................................................49

16. Graphs showing simulated changes in the total phosphorus concentrations 

for the Upper Pool Lakes and Lake Winnebago, in response to various phosphorusloading scenarios (table 13) using the linked Jensen model ..............................................50

17. Graph showing simulated changes in the total phosphorus concentrations 

in Lake Winnebago, in response to various phosphorus-loading scenarios 

using the linked Jensen model, demonstrating beneficial and detrimental 

effects of it being in a chain of lakes.......................................................................................53

Tables

1. Morphometric characteristics of the Winnebago Pool Lakes, Wisconsin, 

on the basis of 2014 Fishing Hotspots Lake Winnebago Map and 2007 Mapping 

Specialists Poygan, Winneconne, Butte des Morts Map......................................................5

2. River and tributary monitoring sites for the Winnebago Pool Lakes and 

their drainage basins ...................................................................................................................7

3. Average June–September near-surface water quality in the 

Winnebago Pool Lakes.................................................................................................................14

4. Summer-average (June–September) near-surface total phosphorus, 

chlorophyll a, Secchi depths, and total nitrogen for Lake Winnebago1976–2015 ...........16

5. Flow, total phosphorus loads, and total phosphorus concentrations 

(volumetrically weighted), and flow and total phosphorus (P) yields in the 

Winnebago Pool tributaries, inlet to Lake Winnebago and outlet of 

Lake Winnebago in water years 2009–14 ...............................................................................19

6. Summary of the water-budget components for Lake Winnebago, 

water years 2009–14...................................................................................................................20

7. Calculation of Soil and Water Assessment Tool ratios used to extraplolate 

measured flows and phosphorus loads at selected sites in the Winnebago 

Pool Basin to unmonitored areas in the basin.......................................................................22

8. Summary of the phosphorus-budget components for Lake Winnebago, 

water years 2009–14 ..................................................................................................................25

9. Summary of the total flow and phosphorus-budget components for the 

Winnebago Pool Lakes, water years 2009–11 .......................................................................26

10. Phosphorus input from septic systems into the Winnebago Pool Lakes, 2011................29

11. Phosphorus release rates in the Winnebago Pool Lakes, August, 2010...........................31

12. BATHTUB simulation results.....................................................................................................35

13. Linked Jensen model simulation results.................................................................................44

14. Parameters and coefficients used in the calibrated Jensen models for 

Lake Winnebago and the three Upper Pool Lakes................................................................45

Figures—Continued
viii

Conversion Factors

International System of Units to U.S. customary units

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

kilometer (km) 0.6214 mile (mi)

micrometer (μm) 0.00003937 inch (in.) 

meter (m) 1.094 yard (yd) 

Area

square kilometer (km2) 0.3861 square mile (mi2)

Volume

cubic meter (m3) 264.2 gallon (gal) 

cubic meter (m3) 35.31 cubic foot (ft3)

Flow rate

cubic meter per year (m3/yr) 0.000811 acre-foot per year (acre-ft/yr) 

cubic meter per day (m3/d) 35.31 cubic foot per day (ft3/d) 

cubic meter per day (m3/d) 264.2 gallon per day (gal/d) 

Mass

kilogram (kg) 2.205 pound avoirdupois (lb)

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

°F = (1.8 × °C) + 32.

Datum

Vertical coordinate information is referenced to the Datum of 1983 (NAD 83).

Supplemental Information

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

or micrograms per liter (μg/L).

Loading or release rates are given in milligrams per square meter per day (mg/m2/d) or 

milligrams per square meter per year (mg/m2/yr).

Yields are given in meters (m) for flow and in kilograms per square kilometer (kg/km2) for nutrient 

constituents.

Deposition rates are given in kilograms per hectare per year (kg/ha/yr).

Inputs are given in kilograms per year (kg/yr).

Sediment volume is given in cubic meters per square meter (m3/m2), bulk density is given in 

grams per cubic meter (g/m3), and mass is given in grams per square meter (g/m2) or milligrams 

per square meter (mg/m2).

Note to USGS users: Use of hectare (ha) as an alternative name for square hectometer (hm2) is 

restricted to the measurement of small land or water areas. Use of liter (L) as a special name for 

cubic decimeter (dm3) is restricted to the measurement of liquids and gases.
ix

Abbreviations

Chl-a chlorophyll-a

DO dissolved oxygen

DP dissolved phosphorus

EGRET Exploration and Graphics for RivEr Trends

NO2+3 nitrate plus nitrite nitrogen as nitrogen

NWIS National Water Information System

P phosphorus

RMSE root mean square error

SD Secchi depth

SWAT Soil and Water Assessment Tool

SWIMS Surface Water Integrated Monitoring System database

TKN total Kjeldahl nitrogen

TMDL Total Maximum Daily Load

TN total nitrogen

TP total phosphorus

TSI trophic state index

WDNR Wisconsin Department of Natural Resources

WRTDS Weighted Regressions on Time, Discharge, and Season program

WSLH Wisconsin State Laboratory of Hygiene

WQ water quality

WY water year (the period from October 1 to September 30 of the specified year)

USDA–ARS U.S. Department of Agriculture Agricultural Research Service

USGS U.S. Geological Survey

z mean lake depth

Water-Quality Response to Changes in Phosphorus 

Loading of the Winnebago Pool Lakes, Wisconsin, 

with Special Emphasis on the Effects of Internal Loading 

in a Chain of Shallow Lakes

By Dale M. Robertson,1 Benjamin J. Siebers,1 Matthew W. Diebel,2 and Andrew J. Somor3

1

U.S. Geological Survey.

2

Wisconsin Department of Natural Resources.

3

The Cadmus Group.

Abstract

The Winnebago Pool is a chain of four shallow lakes 

(Lake Poygan, Lake Winneconne, Lake Butte des Morts, and 

Lake Winnebago) that are fed primarily by the Fox and Wolf 

Rivers, two large agriculturally dominated rivers in Wisconsin, 

United States. Because the lakes have received extensive phosphorus inputs from their watershed, they have become highly 

eutrophic with much phosphorus in the water column as well 

as trapped in their sediments. Each of the four Winnebago 

Pool Lakes has been included on the Wisconsin Department of 

Natural Resources impaired waters list because of their high 

total phosphorus concentrations, water-quality use restrictions, 

and excess algal growth. The study described in this report is 

part of a Total Maximum Daily Load investigation to determine what actions are needed to improve the water quality 

(trophic status) of these lakes and thus be able to be removed 

from the impaired waters list and restore their designated uses. 

As part of this study, data were collected to describe the existing water quality of the lakes, detailed phosphorus budgets 

were developed for each of the lakes to describe the different 

sources of the phosphorus, and two eutrophication models 

(BATHTUB and Jensen models) were used to determine how 

much of the phosphorus being input to the lakes needs to be 

reduced for the lakes to be removed from the impaired waters 

list and restore their designated uses.

In-lake water-quality data indicated that each of the 

lakes had extensive vertical mixing that resulted in their water 

quality deteriorating throughout summer. Each of the lakes 

had mean summer total phosphorus concentrations exceeding 

0.088 milligram per liter (mg/L), well above the 0.040 mg/L 

criterion for the lakes. Detailed phosphorus budgets for the 

lakes indicated that the primary sources of phosphorus were 

from their tributaries (for the most upstream lake in the 

Winnebago Pool–Lake Poygan) or from a combination of 

input from the upstream lakes and phosphorus release from the 

bottom sediment when only the summer months were considered (for the other three lakes).

Model simulations with the BATHTUB and Jensen 

models indicated that (1) the lakes should have almost linear 

response in their total phosphorus concentrations to changes 

in their phosphorus inputs; (2) phosphorus inputs need to be 

reduced by about 60 percent to the Upper Pool Lakes and 

69–73 percent to Lake Winnebago to reduce their mean summer total phosphorus concentrations to 0.040 mg/L; and (3) if 

all the anthropogenic phosphorus inputs to the lakes could be 

eliminated, their best possible mean summer total phosphorus 

concentrations should decrease to about 0.022–0.028 mg/L in 

the Upper Pool Lakes and to 0.032–0.033 mg/L in Lake Winnebago. The effects of any reduction in phosphorus loading 

will take many years (50 to more than 75 years) to be fully 

realized in lake water quality because of phosphorus release 

from the lake sediments. The effects of nutrient reductions 

in the watershed of a chain of lakes, such as the Winnebago 

Pool, gradually cascades down the chain, which has beneficial 

and detrimental effects. Any action made in the watershed of 

upstream lakes to reduce phosphorus inputs should improve 

the water quality of all downstream lakes; however, the 

upstream lakes delay the response in the downstream lakes, 

especially in lakes where internal phosphorus loading is 

important.

Introduction

The Winnebago Pool (also referred to as the “Pool 

Lakes”) is a chain or series of four shallow lakes (Lake 

Poygan, Lake Winneconne, Lake Butte des Morts, and Lake 

Winnebago) primarily fed by the Fox and Wolf Rivers, two 

large agriculturally dominated rivers in Wisconsin, United 

States (fig. 1). The water quality (WQ) in these lakes, like 

many other lakes in agricultural areas, has declined (enhanced 
2 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

eutrophication) because of excessive phosphorus (P) input 

from their watersheds (Wisconsin Department of Natural 

Resources, 2004; Schindler and others, 2016). Because of high 

total phosphorus concentrations (TP), all four Pool Lakes, 

which are classified as “shallow lowland drainage” lakes, were 

officially listed as “impaired” (mean June through September 

TP greater than 0.040 milligram per liter [mg/L]; Wisconsin 

Department of Natural Resources, 2016, 2017a), and a Total 

Maximum Daily Load investigation is being done to determine 

what actions are needed to improve their WQ and restore their 

designated uses. Designated uses for the Winnebago Pool, as 

defined by the Wisconsin Department of Natural Resources 

(WDNR), are for fish and aquatic life, recreational use, public 

health and welfare, and wildlife. The lake indicators of high 

TP are eutrophication, water-quality use restrictions, and 

excess algal growth. The Total Maximum Daily Load calculation is complicated by the short-term (annual) and long-term 

(multi-year) effects of P released from the bottom sediments 

in these shallow lakes and the effects of nutrient reductions 

cascading through the chain of lakes.

Many factors affect a lake’s trophic state (including TP 

and chlorophyll-a [Chl-a] concentrations) and water clarity (Secchi depth [SD]). Usually, the main factor is external 

nutrient input from the watershed that varies with hydrology, 

geology, and long-term anthropogenic changes in the watershed. The effects of nutrient inputs (primarily P for most lakes; 

Schindler and others, 2016) are sufficiently understood such 

that many eutrophication models have been developed to estimate in-lake TP, Chl-a, and SD from their morphometry and 

external water and P loading (mass input during a specified 

period) (Cooke and others, 1993). Most of these eutrophication models describe the response in a single lake; only a few 

models describe the response in a chain of lakes. The BATHTUB model (Walker, 1996) has transport algorithms and can 

simulate changes in complex multibasin lakes or a chain of 

lakes. Other lake-specific empirical models (such as Carpenter 

and Lathrop, 2014) and complex mechanistic models (such as 

Epstein and others, 2013) have been developed for chains of 

lakes.

External P loading drives in-lake TP and productivity, 

and then the P is either exported out of the lake or deposited 

in the sediments. Not all P remains in the sediments; some is 

released back into the water column, referred to as “internal 

P loading.” Some of the P in the bottom sediments can be 

released back into the water column when the water is aerobic 

(contains dissolved oxygen [DO]); however, when deep water 

of a productive lake (a lake with abundant plants or algae) 

becomes isolated from surface mixing because of thermal 

stratification, the sediment and the bottom water often become 

anaerobic or devoid of DO and the rate of internal P loading 

often increases dramatically (Mortimer, 1941). Internal P loading increases with increasing length of stratification (Kling 

and others, 2003), increasing water temperatures that promote 

microbial decomposition (James and Barko, 2004; Jensen and 

others, 2006), and increasing amounts of readily available P in 

the sediment (Rydin and Welch, 1999).

Productivity of shallow lakes, however, may respond differently than deep lakes because of internal P loading. Shallow 

lakes, lakes with a maximum depth less than 6 meters (m), 

typically experience deep mixing events throughout summer 

and are, therefore, referred to as polymictic lakes (Osgood, 

1988). Osgood (1988) described the functional aspects of 

mixing from wind forcing based on a lake’s mean depth (z̄, in 

meters) and surface area (A, in square kilometers) in terms of 

the Osgood Index defined as z̄ ÷ A0.5. Lakes with Osgood Index 

values less than 4 tend to be polymictic. Typically, P released 

from deep sediments in deep dimictic lakes (that is, lakes that 

remain stratified during the summer months) is retained in the 

hypolimnion (that is, the cool, lower layer of water in the lake) 

during summer and primarily released to near the surface of the 

water column during spring and fall turnover. Therefore, nearsurface TP in dimictic lakes usually remains stable or decreases 

as summer progresses (Welch and Cooke, 1995). In shallow 

polymictic lakes, microzones of anaerobic activity can develop 

at or just below the sediment-water interface during the short 

periods of stratification. Then, frequent deep mixing events 

can cause an upward transport of the P, resulting in warmer 

bottom water and near-surface TP and productivity increasing 

throughout summer (Welch and Cooke, 1995). Robertson and 

others (2016) demonstrated differences in bottom temperatures 

and in surface TP and Chl-a between deep and shallow lakes 

by comparing the WQ in morphologically different basins in 

a multibasin lake in northern Wisconsin. In addition to mixing 

of the water column, strong winds can cause sediment resuspension that can increase sediment P release in shallow lakes 

(Søndergaard and others, 1992; Cyr and others, 2009; Huang 

and others, 2016). Søndergaard and others (1992) estimated 

that resuspension could enhance the rate of soluble P release 

from the sediment by 20–30 times compared to undisturbed 

sediment. In addition, aquatic animals can directly affect the 

cycling of P and increase internal P loading in lakes through 

feeding (which stirs up the sediments) and excretion (Andersson and others, 1988; Fischer and others, 2013). Based on 

enclosure studies, common carp (Cyprinus carpio) contribute 

as much as 4.4 percent (Lamarra, 1975) of their body weight as 

P per year into the water column. Fish feeding activity, which 

often uproots vegetation, also can create more flocculent sediments that are more prone to suspension from wind (Lin and 

Wu, 2013), thus increasing internal P release into a lake.

Lakes with high internal P loading may respond much 

slower to reductions in external P loading than other lakes 

(Jeppesen and others, 2005, Jensen and others, 2006, Meals 

and others, 2010). Even 20 years after large external P reductions, internal P loading continued to affect the trophic state 

of Shagawa Lake in Minnesota (Seo and Canale, 1999). Most 

eutrophication models do not simulate the transient effects 

of changes in external P loading; however, Jensen and others 

(2006) developed a simple empirical model that describes the 

continuous changes in in-lake TP and in-sediment P after external load reductions, which is a function of external P loading, 

initial available P in the sediment, hydraulic residence time, 

and water temperature.
nm

X

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88°30'

88°30'

89°

89°

44°15'

44°

43°

3 1

2

3

1

3

2

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0 2.5 5 10 KILOMETERS

0 2.5 5 10 MILES

X

nm

!

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Drainage basinDrainage subbasinBathymetric contour— Depth in metersLake sampling siteGaging and sampling stationRiver sampling siteWater level stationBuoySediment core site

EXPLANATION

3

Winnebago Pool Lakes, Wisconsin

#

#

#

#

#

*#

89°

89°

90°

90°

45° 45°

44°

44°

0 12.5 25 50 KILOMETERS

0 12.5 25 50 MILES

Fond du Lac

River

L

a

ke

Winn

ebago

Lake Poygan

Lake 

Butte des

Morts

 LakeWinneconne

Wolf River

Lake Poygan

Lake Butte des Morts

Lake Winneconne

W

Appleton

Upper

Fox River

Berlin

New London

Wolf

River

Fond du Lac

Oshkosh 

Neenah 

M

Upper Fox River

! !

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3

2

1

Base from U.S. Geological Survey digital data, 1:250,000, 1994 North American Datum of 1983 HARNTransverse Mercator projectionCentral meridian 90°WScale factor 0.9996Latitude of origin 0.0

Lorem ipsum

Figure 1. Winnebago Pool Lakes and their watersheds, with sampling locations identified, Wisconsin. Sampling sites are described in Table 2. Lake 
4 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

Typically, lakes are considered to be singular entities in 

the environment (Forbes, 1887) and are modeled that way. In a 

chain of lakes, such as the Winnebago Pool, however, the lakes 

interact; changes upstream in the watershed cascade down 

the chain. Lathrop and Carpenter (2014) and Carpenter and 

Lathrop (2014) modeled the effects of nutrient reduction strategies implemented in various parts of the Yahara watershed, 

Wisconsin, United States, cascading down through a chain of 

lakes. In a chain of lakes, actions done upstream in the watershed improve the WQ of all the downstream lakes; however, 

the response to external P load reductions also can be delayed 

in the downstream lakes, especially where internal loading is 

an important part of their P budget (Jeppesen and others, 2005; 

Jensen and others, 2006; Meals and others 2010).

Purpose and Scope

The purpose of this study was to (1) document the present (2009–11) WQ of each of the Winnebago Pool Lakes, 

(2) describe their water and P budgets including quantifying 

internal P loading using various approaches, (3) determine how 

the WQ of each lake should respond to changes in P loading 

(steady state and transient changes) using the BATHTUB and 

Jensen eutrophication models, (4) determine how much of the 

present P inputs would have to be reduced to attain nonimpairment and thus be able to delist each of the Pool Lakes for high 

TP, and (5) estimate the WQ in the lakes if all anthropogenic 

P inputs were removed (best attainable WQ). Because the 

Winnebago Pool is a chain of shallow lakes where internal 

P loading is expected to be important, specific approaches 

were used to determine how the trophic response to changes in 

P loading cascades down the chain and how internal P loading 

affects the steady state and transient responses of these lakes.

Methods

Study Area

The Winnebago Pool consists of four shallow lakes: Lake 

Poygan (58 square kilometers [km2]; mean depth [z̄]=1.8 m; 

the most upstream lake), Lake Winneconne (19 km2; z̄=1.6 m), 

Lake Butte des Morts (35 km2; z̄=1.6 m), and Lake Winnebago 

(532 km2; z̄=4.5 m; the most downstream lake) (fig. 1; table 1). 

Lakes Butte des Morts and Winnebago are connected by a 

4.6-kilometer (km) widening of the Fox River. The Winnebago 

Pool has three main tributaries: Wolf River that drains into 

Lake Poygan, Fox River that drains into Lake Butte des Morts, 

and Fond du Lac River that drains into Lake Winnebago. Collectively, the Pool Lakes drain more than 14,000 km2

 of central 

Wisconsin before discharging into the lower Fox River, which 

is one of the largest tributaries to Lake Michigan. The watersheds of all the lakes are dominated by agriculture (table 1), 

but the Wolf River Basin upstream from Lake Poygan has more 

forested land than other areas, and the land immediately around 

Lake Winnebago has more urban development than other areas, 

including the cities of Oshkosh and Fond du Lac (fig. 1).

All four Pool Lakes were included on the WDNR 2016 

impaired waters list for TP and suspended sediment (Wisconsin Department of Natural Resources, 2016). All four lakes 

are classified as “shallow lowland drainage” lakes with a TP 

criterion defined as mean TP concentration between June 1 and 

September 15 to not exceed 0.040 mg/L (Wisconsin Department of Natural Resources, 2017a).

Data Collection

Lake Water Quality

As part of this study, historical WQ (TP, Chl-a, and SD) 

data for each of the Pool Lakes were assembled, but only 

historical data for Lake Winnebago are presented in this report 

because of the lack of consistent data available for the other 

lakes. Because of their shallow depths, usually only surface 

WQ data are collected. Each of the Pool Lakes was originally 

sampled monthly as part of a University of Wisconsin-Oshkosh 

study from June 1976 to May 1977 (Sloey and Spangler, 1977). 

WQ in Winnebago was then consistently measured from 1989 

to 2015 as part of the WDNR Long-Term Trend monitoring 

program; however, only limited sampling was done in the other 

Pool Lakes. The lakes also were sporadically sampled by local 

citizens as part of the WDNR Citizen Lake Monitoring Program 

(Wisconsin Department of Natural Resources, 2018); however, 

usually only SDs were measured. These data were obtained 

from the WDNR Surface Water Integrated Monitoring System 

(SWIMS) database at https://dnr.wi.gov/topic/surfacewater/

swims/ (Wisconsin Department of Natural Resources, 2017b). 

The north end of Lake Winnebago also was sampled as part 

of limnological studies by Lawrence University (B. DeStasio, 

Professor, Lawrence University, unpub. data). The historical 

WQ data for Lake Winnebago are available at https://doi.

org/10.5066/P9Y8BE4H (Robertson and Kennedy, 2018).

As part of this study, each of the Pool Lakes was sampled 

monthly by the WDNR during May through September 

2009–11 near their deepest locations, except Lake Winnebago, 

which was sampled at three locations (fig. 1). During each visit, 

consistent protocols, similar to the WDNR Long-term Trend 

Monitoring Program (Wickman and Herman, 2005) protocols, 

were used that involved collecting profiles of water temperature, DO, specific conductance, and pH with a multiparameter 

meter, and collecting SD with a standard 20-centimeter (cm) 

diameter black and white Secchi disk. Near-surface grab samples were collected and analyzed for TP, dissolved phosphorus 

(DP), dissolved nitrite plus nitrate (NO2+3), total Kjeldahl 

nitrogen (TKN) and Chl-a by the Wisconsin State Laboratory of Hygiene (WSLH; Madison, Wis.) in accordance with 

standard analytical procedures (Wisconsin State Laboratory of 

Hygiene, Environmental Science Section, 1993). All WQ data 

were obtained from the WDNR SWIMS database at

https://dnr.wi.gov/topic/surfacewater/swims/

(Wisconsin Department of Natural Resources, 2017b).
Table 1. Morphometric characteristics of the Winnebago Pool Lakes, on the basis of 2014 Fishing Hotspots Lake Winnebago Map (https://www.fishi

pc/ viewPrd.asp?idproduct=311) and 2007 Mapping Specialists Poygan, Winneconne, Butte des Morts Map (https://www.mappingspecialists.com/ stowinneconne-lake-butte-des-morts-fold-map/).[m, meter; km, kilometer; km2, square kilometer; km3, cubic kilometer] 

Lake or river

Primary 

water-quality 

station number

Maximum 

depth

(m)

Mean 

depth 

(m) 

Fetch

(km)

Area

(km2)

Volume

(km3)

Residence 

time

(daysa)

Osgood 

index

Lake 

drainage 

area

(km2)

S

dra

(

Poygan 713121 3.35 1.78 12.4 58.0 0.103 13.2 0.23 9,455 Winneconne 713282 3.96 1.61 7.6 19.1 0.031 4.07 0.37 (Included wButte Des Morts 713252 3.66 1.56 11.3 35.4 0.055 3.7 0.26 13,510 9Fox River—Connecting 713056 8.00 2.24 4.6 2.1 0.058 0.4 1.56 13,560 13Winnebagoc— 6.40 4.54 45.3 532.3 2.415 187.5 0.20 14,290 14 Center site 713245d North site 713243e South site 713244f

aBased on total annual water inputs from water years 2009–11.bBased on data from the National Land Cover Database (Fry and others, 2006).cSummary statistics for Winnebago were computed for the entire lake, but data were collected at three stations.dFor long-term analysis the following station numbers were also included: 713302, 713338, 713339, 713342, 713355, and 714005.eFor long-term analysis the following station numbers were also included: 713301 and 713329.fFor long-term analysis the following station numbers were also included: 203101 and 203110.
6 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

All historical average monthly and seasonal WQ data for 

Lake Winnebago were obtained by averaging available data 

from the north, center, and south parts of the lake (station numbers for each location are given in table 1). To reduce potential 

biases from nonuniform sampling through time, individual 

WQ values were averaged monthly and then summer-average 

(June–September) WQ was computed from the monthly values; 

months with missing data were estimated by using the longterm (1973–2015) average for the missing month.

One method of classifying the WQ of a lake is with 

trophic state index (TSI) values based on near-surface concentrations of TP and Chl-a, and SD, as developed by Carlson 

(1977), and total nitrogen (TN), as developed by Kratzer and 

Brezonik (1981). The indices were developed to place these 

four characteristics on similar scales to allow trophic comparisons among constituents. TSI values based on TP (in milligrams per liter; TSITP), Chl-a (in micrograms per liter; TSIChl-a), 

SD (in meters; TSISD), and TN (in milligrams per liter; TSITN) 

were computed for each sampling date using equations 1–4. 

Individual TSI values were averaged monthly, and the monthly 

average values were then used to compute summer-average 

(May through September) TSI values:

 TSITP 4.15 + 14.42 × (ln [TP × 1,000]) (1)

 TSIChl-a = 30.6 + 9.81 × (ln Chl-a) (2)

 TSISD = 60 – 14.41 × (ln SD) (3)

 TSITN = 54.45 + 14.43 × (ln TN) (4)

Oligotrophic lakes have TSI values less than 40; have a 

limited supply of nutrients; typically have low TP, low algal 

populations, and good water clarity; and contain DO throughout the year in their deepest zones (Carlson and Simpson, 

1996). Mesotrophic lakes have TSI values from 40 to 50; have 

a moderate supply of nutrients; tend to produce moderate algal 

blooms and moderate clarity; and occasionally have DO depletions in the deepest zones of the lake. Eutrophic lakes have 

TSI values greater than 50; have a large supply of nutrients; 

have severe WQ problems, such as frequent seasonal algal 

blooms and poor water clarity; and commonly have DO depletions throughout the deeper zones of the lake. Eutrophic lakes 

with TSI values greater than 70 often are classified further as 

hypereutrophic, and they typically have even more severe WQ 

problems, including frequent extensive algal blooms.

Lake Morphometry

Morphometric characteristics of Lake Winnebago 

were based on the 2014 Fishing Hotspots Lake Winnebago 

Map (https://www.fishinghotspots.com/e1/pc/viewPrd.

asp?idproduct=311). Morphometric characteristics for the 

three Upper Pool Lakes (Lake Poygan, Lake Winneconne, 

and Lake Butte des Morts) were based on the 2007 Mapping Specialists Poygan, Winneconne, Butte des Morts Map 

(https://www.mappingspecialists.com/store/lake-poyganlake-winneconne-lake-butte-des-morts-fold-map/). The 

surface areas and associated contour lines for the lakes were 

reevaluated and adjusted, if needed, on the basis of an aerial 

image obtained from the 2005 National Agricultural Imagery 

Program (U.S. Department of Agriculture, 2006). The area 

and volume of the lake at specific depths were computed from 

the depth contours of the map using a geographic information 

system (GIS).

Lake Stage

Daily water levels of Lake Winnebago have been 

measured near to where the Fox River enters Lake Winnebago 

(USGS station 04082500; fig. 1) since 1882. The U.S. Geological Survey (USGS) has monitored water levels at this location 

with a stage gage since 1938. Data from October 2008 to September 2014 were used in this study. All water-level data were 

obtained from the National Water Information System (NWIS) 

database at https://doi.org/10.5066/F7P55KJN (U.S. Geological Survey, 2018).

River and Tributary Monitoring and Load 

Computation

Five river sites (fig. 1; table 2) were instrumented to 

monitor flow continuously (at 5- to 15-minute intervals) and 

to estimate P loading at selected locations in the watershed or 

downstream from the lakes. At three sites (Wolf River at New 

London, Fox River at Berlin, and Fond du Lac River at Fond 

du Lac), water levels were measured and used to determine 

flow using standard stage-discharge relations (Rantz and others, 1982). Flow at the Fox River at Oshkosh (upstream from 

Lake Winnebago) and Fox River at Appleton (downstream 

from Lake Winnebago and used to estimate flow out of the 

lake at Neenah Menasha) were estimated using acoustic Doppler velocity meters and water-level sensors (Sauer, 2002) 

because backwater conditions did not enable flow to be estimated solely from changes in water elevation. Each site has 

been in operation since at least 1986, except the Fond du Lac 

River site, which was operated from 2007 to 2011. From the 

5- to 15-minute flow data, daily average flows were computed. 

All flow data were obtained from the National Water Information System (NWIS) database at https://doi.org/10.5066/

F7P55KJN (U.S. Geological Survey, 2018).
Table 2. River and tributary monitoring sites for the Winnebago Pool Lakes and their drainage basins, Wisconsin.

[km2, square kilometer; WDNR ID, Wisconsin Department of Natural Resources station identification number; Wis., Wisconsin; WRTDS, Weighted Regressions on Time, DischGCLAS, Graphical Constituent Loading Analysis System]

USGS station name

USGS

station 

number

Drainage 

area (km2)

Streamflow 

period of 

record

Waterquality station 

WDNR ID

Used 

water-quality 

data

Water-quality 

sampling 

frequency

Increased frequency 

during study

co

t

Wolf River at New London, Wis. 04079000 6,123 1913–2018 693035 1977–2014 Monthly About 3 times per 

month in 2010–12

WRT

Fox River at Berlin, Wis. 04073500 3,427 1898–2018 243020 1977–2014 Monthly About 3 times per 

month in 2008–11

WRT

Fox River at Oshkosh, Wis. 04082400 14,070 1991–2018 713056 2009–14 Monthly No extra sampling LineaFond du Lac River at Fond du Lac, 

Wis.

04083545 435 2007–11 04083545 2008–11 About 40 

times per year

No extra sampling GCLA

Fox River at Neenah Menasha,a Wis. 04084445b 15,570 1986–2018 713002 2009–14 Monthly About 4 times per 

month in 2011–12

Linea

aNeenah and Menasha are technically two cities on opposite sides of the riverbStreamflow from Fox River at Appleton was used for this site, with with adjustment factors described in the text.
8 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

Samples for WQ analyses (TP) for all river sites, except 

the Fond du Lac River, were collected on a routine monthly 

basis using grab or equal-width increment methods (Edwards 

and Glysson, 1999) by the USGS or WDNR. As part of this 

study, additional samples were collected about weekly during 

a few years at all sites, except the Fox River at Oshkosh site, 

to better describe changes in concentrations. Samples at the 

small Fond du Lac River site with quickly changing flows 

were collected throughout high-flow events using an automated sampler and augmented by routine base-flow samples. 

All chemical analyses were done by the WSLH in accordance 

with standard analytical procedures (Wisconsin State Laboratory of Hygiene, Environmental Sciences Section, 1993). 

All river TP data are available from the WDNR SWIMS database at https://dnr.wi.gov/topic/surfacewater/swims/

(Wisconsin Department of Natural Resources, 2017b) 

or NWIS database at https://doi.org/10.5066/F7P55KJN

(U.S. Geological Survey, 2018).

Because TP concentrations at the various riverine sites 

had different responses to changing flow conditions, different approaches were used to compute TP loads at each site. 

Daily TP loads for the Fox River at Oshkosh and Fox River at 

Neenah Menasha for water years (WY) 2009–14 were computed using a simple linear interpolation technique to estimate 

daily TP concentrations between measured concentrations 

because changes in concentrations downstream from the lakes 

varied slowly and had little relation to streamflow. Daily loads 

were then computed as the product of daily concentration and 

daily discharge. Daily TP loads at the Fond du Lac River site, 

with quickly changing flows, were computed for WY2009–11 

using the Graphical Constituent Loading Analysis System 

(GCLAS; Koltun and others, 2006). GCLAS was developed to 

estimate loads of WQ constituents from continuous measurements of streamflow and instantaneous constituent concentrations. Generally, concentrations are linearly extrapolated 

between measurements except at the beginning and end of 

events with large changes in flow. Before the extrapolations, 

additional concentrations often are added to the time series 

to better describe the concentrations just before and after an 

event or to describe events without measured concentrations. 

The filled-in concentrations at the beginning of an event were 

estimated from concentrations measured during previous 

low-flow periods. Concentrations at the end of the events were 

estimated from concentrations measured shortly after the end 

of an event. Daily loads for WY2012–14 (unmonitored period) 

for the Fond du Lac River were estimated from measured 

daily flows multiplied by the volumetrically weighted concentration of the WY2009–11 period. Daily TP loads during 

WY2009–14 at the Wolf River at New London and Fox River 

at Berlin were computed using the Weighted Regressions 

on Time, Discharge, and Season program (WRTDS; Hirsch 

and De Cicco, 2014) using all available TP data for these 

sites from 1977 to 2014. WRTDS was implemented using 

the R Package (R Development Core Team, 2013) Exploration and Graphics for RivEr Trends (EGRET). WRTDS is 

used to develop nonlinear, time-varying relations between the 

logarithms of the constituent concentrations and explanatory 

variables consisting of decimal time, the logarithm of daily 

discharge, and sine and cosine transformations of decimal 

time (Hirsch and others, 2010; Lee and others, 2016). WRTDS 

derives these flexible relations using a unique weighted regression for each day of the estimation period. All default weighting windows in EGRET were used in this study. Weights 

for each day are based on differences in the values of the 

explanatory variables between the estimation and sample day. 

WRTDS uses a bias correction factor specific to each year, 

day, and discharge to adjust for retransformation bias (Hirsch 

and De Cicco, 2014). All daily loads for WY2009–14 for 

these sites are available in the NWIS database at https://doi.

org/10.5066/F7P55KJN (U.S. Geological Survey, 2018).

Sediment P Release

Sediment P release from diffusion and sediment resuspension were estimated separately. To estimate the release 

rates of P from the lake sediments from diffusion alone during aerobic and anaerobic conditions (used to obtain initial 

internal loading estimates), sediment cores were collected 

with a Wildco® sediment-core sampler at 6 locations in Lake 

Winnebago (12 cores for aerobic and 6 cores for anaerobic 

analyses), 4 locations in Lake Butte des Morts (5 aerobic 

and 5 anaerobic analyses), 2 locations in Lake Winneconne 

(3 aerobic and 1 anaerobic analyses), and 3 locations in Lake 

Poygan (4 aerobic analyses) on August 10, 2010 (fig. 1). 

Anaerobic analyses were only done for cores collected at the 

deeper locations. In the laboratory, cores were maintained in 

either aerobic or anaerobic environments by gently bubbling 

air (aerobic) or nitrogen (anaerobic) through air stones placed 

just above the sediment interface. Samples for DP analysis 

were collected daily for 9 days from water above the sediment 

in each core and filtered through a 0.45-micrometer filter. 

All core processing and chemical analyses were done by the 

WSLH in accordance with standard analytical procedures 

(Wisconsin State Laboratory of Hygiene, Environmental Sciences Section, 1993). P release rates were calculated as the 

linear change in the P mass in the overlying water divided by 

the time and cross-sectional area of the incubation core (James 

and Barko, 1991; Robertson and others, 2012) and were combined to obtain average aerobic and anaerobic release rates for 

each lake and for all lakes combined. The area of aerobic and 

anaerobic conditions at the sediment-water interface is needed 

to determine what areas to apply the aerobic and anaerobic 

rates to compute the total P release from diffusion. This information was obtained from data collected at a buoy installed in 

Lake Winnebago (fig. 1) using NexSens T-Node temperature 

(NexSens Technology, Inc.) and RDO PRO® DO (In-Situ, 

Inc.) sensors placed at the sediment interface and about every 

meter to the surface of the lake. Each of the sensors was monitored every 5 minutes from May 10 to October 20, 2012. All 

temperature and DO data are available in the NWIS database 

at https://doi.org/10.5066/F7P55KJN (U.S. Geological Survey, 

2018).
Methods 9

Total net internal P release, defined as P released from 

diffusion plus P released from sediment resuspension caused 

by strong winds and biological activity minus sedimentation 

to the lake bottom, was estimated for Lake Winnebago as 

the residual in a detailed P budget constructed for the lake. 

Because all the other terms in Lake Winnebago’s P budget 

could be estimated accurately, the net P release rate could be 

estimated by adjusting the net release rates until estimated TP 

concentrations in the lake matched those measured in the lake 

during WY2009–14. The net P sediment release rates in all 

four lakes also were estimated using BATHTUB by adjusting 

internal loading rates until estimated TP concentrations in the 

lake matched those measured during May through September 

in 2009 through 2011. Since the total inputs to the Upper 

Pool Lakes could not be estimated as accurately as Lake 

Winnebago, their internal P loading rates could not be estimated as accurately as Lake Winnebago. Net P release rates, 

as well as gross P release and sedimentation, in all four lakes 

also were estimated from calibrated Jensen models (described 

later in the “Jensen Model” section).

Meteorological Data

Daily precipitation and air temperature data from October 

2008 to December 2014 for all four Pool Lakes were obtained 

from the National Weather Service station at Oshkosh, 

Wis. (Cooperative Observer Program identification number 

476330) (Midwest Regional Climate Center, 2015).

Numerical Watershed and Lake Models

Watershed Model—SWAT

To estimate the total P loading from the watershed to each 

Pool Lake, the P loads estimated at the monitored sites were 

extrapolated to the complete watershed by using output from 

the Soil and Water Assessment Tool (SWAT) model developed 

for the Upper Fox and Wolf River Basins (The Cadmus Group, 

2018). SWAT is a continuous time step, semidistributed, 

process-based watershed model developed by the U.S. Department of Agriculture Agricultural Research Service (USDA–

ARS; Arnold and others, 2012). SWAT includes key components contributed from several other USDA–ARS models. The 

SWAT model was calibrated and verified with streamflow and 

P loads measured at the five monitored sites included in this 

study and data from several additional small sites monitored 

in the basin, and then the SWAT model was used to estimate 

streamflow and TP loading throughout the Winnebago Pool 

watershed during WY2009–13 (The Cadmus Group, 2018).

Flow and P loading from the SWAT model were applied 

in this study using two different approaches: one for lakemodel calibration and one for full lake-model prediction. For 

lake-model calibration, measured flows and loads at the monitored sites in the basin were extrapolated to their complete 

basin areas by multiplying the measured loads at the selected 

sites by either a simple drainage ratio (Fond du Lac River to 

its mouth) or a SWAT ratio for Lake Poygan and Lake Butte 

des Morts. A SWAT ratio is the total SWAT modeled flow 

and P load to a lake divided by that estimated by SWAT at an 

upstream gaging station. Downstream extrapolation of measured loads using SWAT ratios was used to reduce potential 

biases in SWAT model results. For the unmonitored nearshore 

area between Lakes Butte des Morts and Winnebago, the flows 

and loads were directly from SWAT for both applications. For 

the unmonitored nearshore area around Lake Winnebago, flow 

and P loads were obtained using SWAT ratios and the measured data from the Fond du Lac River site for WY2009–11, 

and completely from SWAT estimates when the Fond du Lac 

River was not monitored (WY2012–13). Flows and P loads 

were estimated for May–September 2009–11 for BATHTUB 

model calibration, and for WY2009–13 for Jensen model calibrations. For lake-model simulations, the full SWAT-estimated 

watershed loading to each lake was used, which was based 

on average total May–September loading for WY2009–13 for 

the BATHTUB model and the full year of monthly loads for 

WY2009–13 for the Jensen models.

Lake Models

Mass-Balance Model

To help estimate net internal P loading (from diffusion 

plus sediment resuspension and other internal sources minus 

sedimentation) to the lakes, a daily TP mass-balance model 

(eq. 5) was constructed for Lake Winnebago for WY2009–14:

ΔTP × Vol = (SWPIn + PPTP + GWPIn + PtP + SepticP + SedPIn) – 

 (SWPOut + GWPOut + SedPOut) (5)

where

ΔΤP is the change in TP concentrations in the 

water column,

Vol is the volume of the lake, in cubic meters,

SWPIn is the surface-water inputs of P,

PPTP is the precipitation inputs,

GWPIn is the groundwater inputs,

PtP is the point sources inputs,

SepticP is the inputs from nearby septic systems,

SedPIn is the inputs from the bottom sediments of the 

lake,

SWPOut is the surface-water outputs,

GWPOut is the groundwater outputs, and

SedPOut is the sedimentation to the bottom sediments 

of the lake.

The product of ΔΤP and Vol is the change in the mass of P in 

the lake and is equal to the sum of the P inputs to the water 

column minus the sum of the P leaving the water column. 

Because each component in equation 5 could be accurately 

measured for Lake Winnebago, it is believed that net internal 

P loading (SedPIn–SedPOut) in Lake Winnebago could be accurately estimated.
10 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

BATHTUB Model

Empirical lake models that relate P loading to measured 

WQ characteristics can be used to determine how changes 

in P loading to the Pool Lakes should affect their WQ. These 

models were developed on the basis of data from many different lake systems with specific measures describing lake WQ, 

such as near-surface TP, Chl-a, and SD. Some of these empirical lake models are contained within the BATHTUB model 

(Walker, 1996). The BATHTUB model includes a hydrologic 

transport algorithm and is, therefore, capable of simulating 

changes in complex lakes (multibasin lakes or a chain of lakes 

like the Winnebago Pool). Within BATHTUB, near-surface 

TP was simulated with the Canfield and Bachmann (1981) 

natural-lake equation (eq. 6), which relates hydrology and P 

loading to near-surface TP:

TP (6) L

z L z

A

A

= ÷

× × ( ( ) ÷ + ÷

1 000

0 162 1 0 458

,

. .

τ

where

TP is total P concentration, in milligrams per liter;

LA is the P-loading rate per unit area of the lake, 

in milligrams per square meter per year;

 z is the mean depth of the lake, in meters; and

	 τ is the water residence time, in years.

̄

Chl-a was then estimated from the estimated TP (eq. 6), 

residence time, and a model-estimated light limitation 

(that is the default Chl-a model in BATHTUB; Walker, 1996). 

SD was estimated from estimated Chl-a and a model-estimated nonalgal turbidity (this is the default model in BATHTUB). Normally, the appropriate averaging time period for 

water and constituent mass balance calculations is 1 year 

for reservoirs with relatively long residence times (typically 

greater than about 1 year) or seasonal (May through September) for reservoirs with relatively short residence times 

(Walker, 1996). Because of the short residence time for most 

of the Pool Lakes (table 1), BATHTUB was applied using flow 

and P inputs from May through September (extrapolated to 

12 months by multiplying the seasonal inputs by 2.385) rather 

using inflow data from all 12 months. The model was used to 

simulate average TP for June through September; this is the 

period for which the phosphorus criterion was derived for the 

Pool Lakes (Wisconsin Department of Natural Resources, 

2017a). Because Lake Winnebago had a relatively long residence time compared to the other lakes (table 1), equation 6 

(applied external to BATHTUB) also was used with flow and 

P inputs for the full year to determine if changing its averaging 

period affected its simulated response to changes in P loading.

Jensen Model

BATHTUB can be used to simulate changes in seasonal 

average WQ at a new equilibrium condition; however, it does 

not describe shorter-term variability or transient changes in 

in-lake WQ after the changes in P inputs. To simulate the 

expected transient and equilibrium conditions in the lakes, the 

Jensen model (Jensen and others, 2006) was used. The Jensen 

model is an empirical model (eq. 7) that relates daily changes 

in in-lake TP concentrations (ΔTP, in milligrams per liter) to 

external P loading per unit area of the lake (LA, in grams per 

square meter), initial recyclable P accumulated in the sediment (PSed, in grams per square meter), mean lake depth (z, 

in meters), and water temperature (T, in degrees Celsius) by 

combining its simulations of sediment P release (PR, in grams 

per square meter; eq. 8) and P sedimentation (PS, in grams per 

square meter; eq. 9).

̄

 

∇

TP

Q

Vol f L P eq P eq

z

d A R S

=

× − ( ) 1 × + ( ) − ( ) 9

 PR = bR × (1 + tR)T−20 × PSed (8)

 PS = bS × (1 + tS)T−20 × TP (9)

where 

Q is the inflow to the lake, in cubic meters per 

day;

 Vol is the volume of the lake, in cubic meters;

 fd hydraulic retention time factor equal to 

1/(1 + V Q√ √365);

 bR is the sediment release constant, that is 

multiplied by a temperature dependence 

factor (tR ) and the PSed of the lake 

sediments; and

 bS is the sedimentation constant, that is 

multiplied by a temperature dependence 

factor (tS ), and the TP concentration in the 

lake (TP).

The Jensen model was converted into an Excel worksheet 

and calibrated for WY2009–13 (that is, optimal values were 

determined for bR, tR, bS, tS, and PSed) using measured TP and 

total daily external P loadings to the lake (all P inputs to the 

lake except those from the sediments) using the Solver code in 

Excel®. Two Jensen models were first developed: one model 

for the three Upper Pool Lakes (collectively), and one model 

just for Lake Winnebago. The Upper Pool Jensen model was 

calibrated for WY2009–13 by using the daily total external P 

input to all three Upper Pool Lakes (Lake Poygan, Lake Winneconne, and Lake Butte des Morts) and measured TP at the 

Fox River at Oshkosh as its in-lake TP response variable. The 

Winnebago Jensen model was calibrated by using daily total 

)

(7)

8
Lake Water Quality 11

external P input to Lake Winnebago and TP concentrations 

measured in the center of the lake combined with those measured at the Fox River at Neenah Menasha as its in-lake TP 

response variable. The additional TP data at Neenah Menasha 

were required to describe the full seasonality in TP concentrations. Daily output from the Upper Pool Jensen model was 

then used as input to the calibrated Winnebago Jensen model 

to obtain a linked Jensen model driven by complete watershed 

loading. The Jensen model uses continuous daily flows and P 

inputs from all 12 months. The Jensen models were used to 

simulate daily in-lake TP for the entire year, and geometric 

summer-mean TP concentrations were then computed for the 

TP criterion assessment period (June 1–September 15).

The BATHTUB and Jensen models were first calibrated 

by using loading from the watershed extrapolated from the 

monitored sites to minimize potential model biases and then 

the models were used to simulate specific scenarios using full 

SWAT simulated watershed inputs (and specific modification 

of those inputs) for WY2009–13 as a base-loading condition.

Lake Water Quality

Water temperatures in all the Pool Lakes gradually 

increased as summer progressed. Only weak thermal stratification was observed in the routine monitoring data. Water 

temperatures typically reached 24–26 degrees Celsius (°C) in 

July and August in 2009–11. All four lakes were polymictic, 

resulting in their near-bottom temperatures being similar to 

their surface temperatures. This extensive deep mixing was 

expected given that the Osgood Index (Osgood, 1988) for each 

lake was much less than 4 (table 1). Because Lake Winnebago 

is deeper than the other lakes, it had slightly stronger stratification than the other Pool Lakes. To document short-term 

changes in stratification, continuous recording sensors were 

installed throughout the water column in Lake Winnebago in 

2012 (fig. 1), which further demonstrated only weak thermal 

stratification in the lake (fig. 2). Near-surface DO was near or 

above saturation throughout most of the open-water period. 

DO in the deep areas of all the lakes occasionally declined 

but rarely was measured below 5 mg/L (DO concentrations 

less than 5 mg/L exceed the DO criterion for lakes; Wisconsin 

Department of Natural Resources, 2017a). In 2012, the continuous recording sensors demonstrated that near-bottom DO 

occasionally dropped well below 5 mg/L but rarely dropped 

below 2 mg/L (fig. 2). These hypoxic occurrences were shortlived because of the frequent deep mixing.

Near-surface TP in all four Pool Lakes were relatively 

similar and had distinct seasonality (fig. 3). TP remained 

relatively steady during May and then increased dramatically from June through late September, often reaching 

0.15 mg/L in late summer. During 2009–11, the average 

near-surface summer (June–September) TP was 0.097 mg/L 

in Lake Winnebago, 0.104 mg/L in Lake Butte des Morts, 

0.088 mg/L in Lake Winneconne, and 0.094 mg/L in Lake 

Poygan (table 3). TSITP values for the Pool Lakes ranged from 

about 68 to 71; therefore, based on TP, the lakes are classified 

on the border between eutrophic and hypereutrophic and are 

classified as hypereutrophic in late summer. DP concentrations were quite different among lakes. In Lake Winnebago, 

DP gradually increased as summer progressed, typically 

exceeding 0.06 mg/L by late summer; therefore, P does not 

seem to be the factor limiting late summer productivity in 

Lake Winnebago. In the other three lakes, DP typically was 

low (less than 0.01 mg/L), but a few concentrations greater 

than 0.07 mg/L were measured. During 2009–11, summeraverage near-surface DP was 0.029 mg/L in Lake Winnebago, 

0.004 mg/L in Lake Butte des Morts, 0.006 mg/L in Lake Winneconne, and 0.011 mg/L in Lake Poygan (table 3).

TN, computed from the sum of NO2+3 plus TKN, was 

relatively similar among lakes and had little seasonality. 

During 2009–11, summer-average near-surface TN was 

1.23 mg/L in Lake Winnebago, 1.65 mg/L in Lake Butte des 

Morts, 1.39 mg/L in Lake Winneconne, and 1.49 mg/L in Lake 

Poygan (table 3), resulting in TSITN values ranging from 57 to 

62. TN greater than 0.74 mg/L indicates eutrophic conditions 

(Kratzer and Brezonik, 1981); therefore, all four lakes are 

classified as highly eutrophic.

Near-surface Chl-a also had distinct seasonality (increasing throughout summer) and was lower in Lake Winnebago 

than in the other lakes (fig. 3). During 2009–11, summer-average near-surface Chl-a was 30.5 micrograms per liter (μg/L) 

in Lake Winnebago, 52.1 μg/L in Lake Butte des Morts, 

39.8 μg/L in Lake Winneconne, and 36.2 μg/L in Lake Poygan 

(table 3). TSIChl-a values for the Pool Lakes ranged from about 

62 to 68; therefore, based on Chl-a, the lakes are classified as 

highly eutrophic, especially in late summer.

Water clarity consistently decreased as summer progressed, especially in Lake Winnebago; lowest SDs occurred 

in mid-to-late summer (fig. 3). Water clarity in Lake Winnebago was better than in the upstream lakes in early summer, 

but clarity was similar among lakes by late summer. During 

2009–11, summer-average SD was 1.15 m in Lake Winnebago, 0.54 m in Lake Butte des Morts, 0.68 m in Lake Winneconne, and 0.66 m in Lake Poygan (table 3). TSISD values 

for the Pool Lakes ranged from about 60 to 70; therefore, on 

the basis of SD, the Upper Pool Lakes are classified as borderline hypereutrophic.

To determine how WQ during 2009–11 compared with 

other recent years, and whether there were any long-term 

changes, data from 2009 to 2011 were compared with data 

collected in 1976 and 1989–2015 (fig. 4; table 4). Only Lake 

Winnebago had sufficient data for this long-term comparison. 

WQ during 2009–11 was similar or possibly slightly better 

(lower TP and Chl-a, and deeper SD) than the long-term average. The earliest data collected by Sloey and Spangler (1977) 

indicates that the WQ in Lake Winnebago may have improved; 

since 1976, TP seems to have decreased and water clarity has 

improved. However, only 1 year of data were available in 

1976, and little data were available between 1976 and 1989.
12 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

IP-094895_fig 02

28

26

24

22

20

18

16

14

12

10

14

12

10

8

6

4

2

0

0

6

4

2

6

4

2

Temperature, in 

degrees Celcius

Dissolved oxygen, in 

milligrams per liter

2

1 2 1

June 1, 2012 July 1, 2012 Aug. 1, 2012 Sept. 1, 2012 Oct. 1, 2012

Date

June 1, 2012 July 1, 2012 Aug. 1, 2012 Sept. 1, 2012 Oct. 1, 2012

0

Depth above the bottom, in meters Depth above the bottom, in meters

Water temperature

Dissolved oxygen

EXPLANATION

Figure 2. Distributions of temperature and dissolved oxygen in Lake Winnebago, Wisconsin, in 2012. The 1 mg/L and 2 mg/L 

isopleths for dissolved oxygen are identified.
Lake Water Quality 13

IP-094896-FIG 03

Lake Poygan Lake Winneconne Lake Butte des Morts Lake Winnebago—Center

EXPLANATION

Secchi depth, in meters

0

1

2

3

4

Date

01/09 05/09 09/09 01/10 05/10 09/10 01/11 05/11 09/11

Secchi depth

Chlorophyll-a concentration,

in micrograms per liter

0

25

50

75

100

125

150

Chlorophyll a

Total phosphorus concentration,

in milligrams per liter

0.05

0

0.10

0.15

0.20

Total phosphorus

Figure 3. Near-surface total phosphorus, chlorophyll a, and Secchi depths in the Winnebago Pool Lakes, 

Wisconsin, 2009–11.
Table 3. Average June–September near-surface water quality in the Winnebago Pool Lakes, Wisconsin.

[ TSI, trophic state index; --, not available]

Sampling site

Measurement TSI

2009–11 2009–13

Sloey and 

Spangler1

historical 1976

Long term 

1976–2015 2009–11 Long term 1976–2015

Total phosphorus, in milligrams per liter

Lake Poygan 0.094 — 0.136 -- 68.6 --

Lake Winneconne 0.088 — — -- 67.9 --

Lake Butte des Morts 0.104 — 0.155 -- 70.7 --

Lake Winnebago—Fox River inlet 0.103 — -- -- 70.6 --

Lake Winnebago2 0.097 0.116 0.226 0.122 68.9 71.8

Lake Winnebago—Fox River outlet 0.105 — -- -- 69.7 --

Dissolved phosphorus, in milligrams per liter

LakePoygan 0.011 -- -- -- -- --

LakeWinneconne 0.006 -- -- -- -- --

LakeButte des Morts 0.004 -- -- -- -- --

Lake Winnebago—Fox River inlet 0.005 -- -- -- -- --

Lake Winnebago2 0.029 -- -- 0.029 -- --

Lake Winnebago—Fox River outlet 0.045 -- -- -- -- --

Total nitrogen, in milligrams per liter

Lake Poygan 1.49 -- -- -- 60.0 --

Lake Winneconne 1.39 -- -- -- 58.9 --

Lake Butte des Morts 1.65 -- -- -- 61.5 --

Lake Winnebago—Fox River inlet 1.66 -- -- -- 61.6 --

Lake Winnebago2 1.19 -- -- 1.28 57.0 57.7

Lake Winnebago—Fox River outlet 1.23 -- -- -- 56.9 --

Chlorophyll a, in micrograms per liter

Lake Poygan 36.2 -- 90.2 -- 63.7 --

Lake Winneconne 39.8 -- -- -- 64.5 --

Lake Butte des Morts 52.1 -- 47.1 -- 68.3 --

Lake Winnebago—Fox River inlet 45.5 -- -- -- 65.6 --

Lake Winnebago2 30.5 43.5 68.5 48.7 61.6 66.4

Lake Winnebago—Fox River outlet 25.5 -- -- -- 56.4 --

Secchi depth, in meters

Lake Poygan 0.66 -- 0.58 -- 66.7 --

Lake Winneconne 0.68 -- -- -- 66.3 --

Lake Butte des Morts 0.54 -- 0.48 -- 69.7 --

Lake Winnebago2 1.15 1.04 0.66 0.98 59.9 61.5

1

Sloey and Spangler (1977).

2

Average of data collected at north, center, and south sites, whenever available.

14 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin
Lake Water Quality 15

Secchi depth, in meters

Secchi depth

0

0.5

1.0

1.5

Year

1975 1980 1985 1990 1995 2000 2005 2010 2015

Chlorophyll-a concentration, in micrograms per liter

0

25

50

75

100

125

Chlorophyll a

0

0.05

0.10

0.15

0.20

0.25

Total phosphorus concentration,

in milligrams per liter

Total phosphorus

Figure 4. Summer-average near-surface total phosphorus, chlorophyll a, and Secchi depths in Lake Winnebago, 

Wisconsin, 1976–2015.
Table 4. Summer-average (June–September) near-surface total phosphorus, chlorophyll a, Secchi depths, and total nitrogen for 

Lake Winnebago, Wisconsin, 1976–2015. 

[TP, total phosphorus; mg/L, milligram per liter; Chl-a, chlorophyll a; μg/L, microgram per liter; SD, Secchi depths; m, meter; TSI, Trophic State Index (values 

were computed using equations 1 through 4 in the text); ; TN, total nitrogen; NA, not available; water quality data were retreived from the sites described in 

table 1]

Year TP (mg/L) Chl-a (μg/L) SD (m) TN (mg/L) TSITP TSIChl-a TSISD TSITN

1976 0.225 68.6 0.67 NA 81.4 71.3 66.2 NA

1989 NA 48.7 1.06 1.182 NA 67.9 59.5 NA

1990 0.120 41.3 0.93 1.232 72.7 64.9 61.9 57.8

1991 0.142 100.7 0.92 1.794 73.5 72.1 63.0 61.0

1992 NA NA NA NA NA NA NA NA

1993 NA NA 1.00 NA NA NA 60.6 NA

1994 0.085 41.4 1.21 1.239 66.9 62.3 58.2 57.0

1995 0.111 49.7 0.96 1.083 71.3 68.6 61.8 55.5

1996 0.124 71.5 1.09 NA 71.7 69.1 59.2 NA

1997 0.108 45.9 1.03 1.221 70.4 67.1 60.8 57.8

1998 0.089 43.4 1.13 1.176 66.0 64.9 59.8 57.4

1999 0.086 45.9 1.07 1.192 67.3 65.2 59.4 56.3

2000 0.136 56.6 0.75 1.523 74.1 70.1 64.8 60.2

2001 0.118 44.9 0.87 1.138 70.8 67.2 64.0 57.0

2002 0.110 18.2 0.96 1.803 71.9 57.8 62.6 63.0

2003 NA NA 0.86 NA NA NA 63.2 NA

2004 0.129 79.1 1.20 NA 72.9 71.8 61.7 NA

2005 0.156 42.8 0.94 0.982 76.5 67.4 61.4 53.9

2006 0.118 42.7 1.09 NA 71.7 64.3 59.4 NA

2007 0.134 41.0 1.06 1.172 73.9 66.2 59.8 57.3

2008 0.147 42.2 0.92 1.385 74.5 64.6 62.0 59.1

2009 0.082 20.6 1.22 1.165 66.9 59.5 57.5 56.6

2010 0.101 33.9 1.16 1.176 70.4 64.5 58.6 56.6

2011 0.108 37.1 1.07 1.239 70.3 64.1 59.9 57.3

2012 0.164 82.8 0.69 NA 76.5 72.3 67.0 NA

2013 0.125 43.1 1.03 NA 73.1 66.8 60.7 NA

2014 0.121 50.3 0.72 NA 70.5 68.2 64.8 NA

2015 0.095 26.5 0.91 NA 68.4 61.7 61.5 NA

Average 2009–11

2009–11 0.097 30.5 1.15 1.194 69.2 62.7 58.7 56.8

2009–13 0.116 43.5 1.04 1.194 71.4 65.4 60.7 56.8

Long-term average 1976–2015

1976–2015 0.122 48.7 0.98 1.277 71.8 66.4 61.5 57.7

16 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin
Hydrology and Water Budget 17

Hydrology and Water Budget

Because productivity of the Pool Lakes is believed to be 

primarily controlled by P, except in late summer, changes in 

the P inputs should change in-lake TP and affect other trophic 

state constituents, like Chl-a and SD. Almost all P entering 

lakes is transported with water inputs; therefore, to quantify 

P inputs, it is helpful to first accurately quantify the water 

inputs. The water budget for a period of interest for a lake 

may be represented as follows:

 ΔS = (SWIn + PPT + GWIn) – (SWOut + E + GWOut), (10)

where

ΔS is change in the lake water volume, in cubic 

meters per day,

SWIn is the surface-water inflow, in cubic meters 

per day,

PPT is the precipitation, in cubic meters per day,

GWIn is the groundwater inflow, in cubic meters per 

day,

SWOut is the surface-water outflow, in cubic meters 

per day,

E is the evaporation, in cubic meters per day, 

and

GWOut is the groundwater outflow, in cubic meters 

per day.

The complete water budget could be quantified for Lake Winnebago; however, much of the information was not available 

for the other lakes. Therefore, the average-annual and growing-season (May–September) water budgets for WY2009–14 

were estimated for Lake Winnebago, and this information was 

then used to help develop P budgets for all of the Pool Lakes.

Changes in Water Level and Lake Volume

Changes in the volume of Lake Winnebago (fig. 5) were 

determined from continuous water levels measured at the 

lake-stage gage near the Fox River inlet (fig. 1) and from lake 

morphometry based on the 2014 contour map for the lake. 

Water levels and volume varied seasonally and were typically 

highest in early summer and lowest in February. Over the 

entire WY2009–14 period, lake volume changed little overall.

Percentage change from the mean volume

–25

–20

–15

–10

–5

0

5

10

15

Lake volume, in billions of cubic meters

1.7

1.9

2.1

2.3

2.5

2.7

Date

Oct. 2008 Oct. 2009 Oct. 2010 Oct. 2011 Oct. 2012 Oct. 2013 Oct. 2014

Water volume in Lake Winnebago

Estimated water volume

EXPLANATION

Measured volume

Figure 5. Measured and estimated volume of Lake Winnebago, Wisconsin, water years 2009–14.
18 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

Surface-Water Inflow and Outflow

Streamflow was measured at five sites in the watershed 

(fig. 1) and used to estimate average-annual and averagegrowing-season surface-water input and output from the 

Pool Lakes (tables 5 and 6). The magnitudes of the measured 

flows were directly related to the size of the drainage basins 

upstream of the gages. After compensating for the difference 

in drainage areas, flows per unit area (yields) were highest 

at the Fox River at Berlin. In general, flows were highest in 

WY2011, especially in the Wolf River, which resulted in the 

average annual flows for WY2009–11 being slightly higher 

than in other summary periods; however, the years with highest flows during May–September varied among sites.

Either drainage-area ratios (total area of interest divided 

by the area at a gaging station) or SWAT-flow ratios (total flow 

to a lake estimated with SWAT divided by the flow estimated 

at a gaging station with SWAT) based on WY2009–11 results 

were used to extrapolate the flows measured upstream in the 

watershed to the total flows into each lake. Drainage areas of 

the monitored sites and full drainage area for each lake used 

in SWAT are shown in figure 6. To estimate average flows 

for May–September, a SWAT-flow ratio of 1.700 was used 

to extrapolate the flow measured at the Wolf River at New 

London to the total flow into Lake Poygan, 1.152 was used 

to extrapolate the flow measured at the Fox River at Berlin to 

the total flow into Lake Butte des Morts, and 1.375 was used 

to extrapolate the flow measured at the Fond du Lac River 

at Fond du Lac to the total ungaged nearshore flow to Lake 

Winnebago. The measured flows estimated at the monitored 

stations, full drainage areas for each lake, and SWAT-flow 

ratios are given in table 7. To estimate annual flows, a SWAT 

ratio of 1.700 was used to extrapolate flow measured at the 

Wolf River at New London to the total flow into Lake Poygan, 

1.141 was used to extrapolate the measured flow at the Fox 

River at Berlin to the total flow into Lake Butte des Morts, and 

1.399 was used to extrapolate the flow measured for the Fond 

du Lac River to the ungaged nearshore flow to Lake Winnebago (table 7). To estimate the total flows from the Fond du 

Lac River, a 1.011 drainage-area ratio was applied to the data 

measured at the gage just upstream from its mouth.

Outflows from Lake Winnebago (Fox River at Neenah 

Menasha) were estimated from flows measured at the Fox 

River at Appleton station using a 1.01 ratio. The total inflow 

to Lake Winnebago from the Fox and Fond du Lac Rivers, the 

remaining nearshore areas, and the total outflow from the lake 

are given in table 6.

Groundwater

Groundwater inflow to Lake Winnebago was estimated from a regional groundwater-flow model developed for the Lake Michigan Basin (Feinstein and others, 

2010). From this model, estimated direct groundwater 

inflow to Lake Winnebago was 12 million cubic meters 

per year (Mm3/yr; 13.3 cubic feet per second [ft3/s]), 

and estimated seepage out of the lake to groundwater 

was 0.9 Mm3/yr (1 ft3/s), for a net inflow of about 

11 Mm3/yr or 4.6 Mm3 during May–September (table 6; 

D. Feinstein, U.S. Geological Survey, written commun., 2013). 

Groundwater inflow to the other lakes could not be estimated 

directly from this model; therefore, it was assumed that total 

groundwater inflows to Lake Poygan, Lake Winneconne, and 

Lake Butte des Morts were 2, 1, and 3 Mm3/yr, respectively, 

which were based on their relative lengths of shoreline. There 

was assumed to be no losses of lake water to groundwater 

from the Upper Pool Lakes.

Precipitation

During 2009–14, daily precipitation on the surface of the 

lakes was estimated on the basis of measured data from Oshkosh, Wis. Based on data from this site, annual precipitation 

on the surface of each lake ranged from 0.739 m in WY2010 

to 1.068 m in WY2008, and the total precipitation during 

May–September ranged from 0.336 m in WY2009 to 0.692 m 

in WY2010. Annual and seasonal rainfall on the surface of 

Lake Winnebago is given in table 6.

Evaporation

Total annual evaporation from Lake Winnebago (0.95 m) 

was assumed to be similar to that measured in evaporation pan 

measurements at Green Bay, Wis., which is about 45 km north 

of the lake (data were collected during 1956–70; Farnsworth 

and Thompson, 1982). The monthly evaporation rates were 

adjusted to better represent large lakes, like Lake Winnebago, 

with more evaporation in the fall and less in late winter and 

early spring. The total evaporation used for Lake Winnebago 

for May–September (0.71 m) is consistent with that estimated 

by Farnsworth and Thompson (1982) for those months.
Table 5. Flow, total phosphorus loads, and total phosphorus concentrations (volumetrically weighted), and flow and total phosphorus (P) yields in th

tributaries, inlet to Lake Winnebago and outlet of Lake Winnebago in water years 2009–14.[m3/s, cubic meter per second; P, phosphorus; kg, kilogram; VW, volumetrically weighted; TP, total phosphorus; mg/L, milligram per liter; m, meter; kg/km2, kilogram per squar

Water 

year

Wolf River at New London Fox River at Berlin Fond du Lac River at Fond du Lac Fox River @ Oshkosh Fox 

Flow 

(m3/s) P (kg) VW TP (mg/L) Flow (m3/s) P (kg) VW TP (mg/L) Flow (m3/s) P (kg) VW TP (mg/L) Flow (m3/s) P (kg) VW TP (mg/L) Flow (m3/s

Annual summary

2009 36 76,143 0.066 32 81,625 0.081 3.3 17,194 0.166 93 216,298 0.074 101 

2010 47 124,879 0.084 37 101,995 0.088 3.6 27,676 0.241 120 271,839 0.072 129 

2011 73 173,782 0.075 38 91,654 0.077 3.5 16,595 0.149 168 390,218 0.074 171 

2012 46 91,001 0.062 32 72,376 0.072 2.3 11,004 0.150 115 247,118 0.068 121 

2013 50 104,508 0.066 35 84,985 0.077 3.2 14,948 0.150 137 298,135 0.069 138 

2014 59 128,474 0.069 34 83,445 0.077 3.4 16,256 0.150 144 460,969 0.101 160 

2009–14 52 116,464 0.071 35 86,013 0.079 3.2 17,279 0.168 129 314,096 0.076 137 

2009–11 52 124,935 0.075 35 91,758 0.082 3.5 20,488 0.186 127 292,785 0.073 134 

2009–13 51 114,062 0.071 35 86,527 0.079 3.2 17,484 0.171 126 284,721 0.071 132 

May–September

2009 36 38,146 0.081 30 47,396 0.119 2.1 4,912 0.176 79 97,901 0.094 75 

2010 59 87,573 0.112 44 69,889 0.119 4.2 17,728 0.322 164 185,575 0.085 160 

2011 68 87,010 0.097 37 54,221 0.110 2.3 6,704 0.220 168 200,063 0.090 166 

2012 36 36,488 0.076 30 38,837 0.099 1.6 3,256 0.150 90 124,346 0.104 92 

2013 55 61,252 0.084 38 53,515 0.105 2.9 5,653 0.150 144 158,082 0.083 135 

2014 69 81,291 0.089 42 54,723 0.099 4.9 9,690 0.150 172 244,530 0.108 186 

2009–14 54 65,293 0.090 37 53,097 0.109 3.0 7,990 0.195 136 168,416 0.094 136 

2009–11 54 70,910 0.096 37 57,169 0.116 2.9 9,781 0.240 137 161,180 0.090 134 

2009–13 51 62,094 0.090 36 52,772 0.111 2.6 7,650 0.204 129 153,193 0.091 126 

Water 

year

Wolf River at New London Fox River at Berlin Fond du Lac River at Fond du Lac Fox River at Oshkosh Fox R

Flow yield (m) P yield (kg/ km2) Flow yield (m) P yield (kg/ km2) Flow yield (m) P yield (kg/ km2) Flow yield (m) P yield (kg/ km2) Flow 

Annual yields

2009–14 0.268 19.0 0.318 25.1 0.234 39.7 0.290 22.3 0

2009–11 0.269 20.4 0.326 26.8 0.252 47.1 0.284 20.8 0

2009–13 0.261 18.6 0.319 25.2 0.231 40.2 0.283 20.2 0

May–September yields

2009–14 0.117 0.0 0.142 0.0 0.091 0.0 0.128 0.0 0

2009–11 0.117 0.0 0.144 0.0 0.087 0.0 0.129 0.0 0

2009–13 0.110 0.0 0.139 0.0 0.079 0.0 0.121 0.0 0
Table 6. Summary of the water-budget components for Lake Winnebago, Wisconsin, water years 2009–14.

Year Fox River Fond du Lac River Nearshore Groundwater inflow Precipitation Total input Neenah Menasha outlet Evaporation 

Annual water inputs and outputs

Water input and output, in millions of cubic meters

2009 2,930 104 146 12 375 3,570 3,200 485 

2010 3,780 116 162 12 545 4,610 4,070 518 

2011 5,290 113 158 12 391 5,960 5,380 504 

2012 3,640 74 104 12 458 4,290 3,840 504 

2013 4,320 101 141 12 495 5,070 4,360 504 

2014 4,550 110 154 12 565 5,390 5,040 503 

Average 2009–14 4,080 103 144 12 471 4,810 4,320 503 

Average 2009–11 4,000 111 155 12 437 4,710 4,220 502 

Average 2009–13 3,990 102 142 12 453 4,700 4,170 503 

Percentage of total input Percentage of tot

2009–14 84.8 2.1 3.0 0.2 9.8 100 89.5 10.4 

2009–11 84.8 2.4 3.3 0.3 9.3 100 89.3 10.6 

2009–13 84.9 2.2 3.0 0.3 9.6 100 89.2 10.8 

May–September water inputs and outputs

Water input and output, in millions of cubic meters

2009 1,040 28.2 39.4 5.0 178 1,290 996 379 

2010 2,170 55.6 77.8 5.0 368 2,680 2,120 380 

2011 2,220 30.8 43.1 5.0 199 2,500 2,200 379 

2012 1,200 22.0 30.8 5.0 240 1,490 1,220 379 

2013 1,900 38.2 53.4 5.0 232 2,230 1,790 379 

2014 2,270 65.5 91.6 5.0 308 2,740 2,460 379 

Average 2009–14 1,800 40.0 56.0 5.0 254 2,160 1,800 379 

Average 2009–11 1,810 38.2 53.4 5.0 248 2,160 1,770 379 

Average 2009–13 1,710 35.0 48.9 5.0 243 2,040 1,660 379 

Percentage of total input Percentage of tot

2009–14 83.5 1.9 2.6 0.2 11.8 100 82.5 17.4 

2009–11 84.0 1.8 2.5 0.2 11.5 100 82.3 17.6 

2009–13 83.7 1.7 2.4 0.2 11.9 100 81.4 18.6 
Hydrology and Water Budget 21

Base from U.S. Geological Survey digital data, 1:1,000,000, 2018

North American Datum of 1983 HARN

Transverse Mercator projection

Central meridian 90° W

Scale factor 0.9996

Latitude of origin 0.0

88°

88°

89°

89°

45°

45°

44°

44°

#

#

#

0 12.5 25 50 KILOMETERS

#

25 50 0 12.5 MILES

Lake Poygan and Lake Winneconne monitored area

Lake Poygan and Lake Winneconne unmonitored area

Lake Butte des Morts monitored area

Lake Butte des Morts unmonitored area

Lake Winnebago monitored nearshore area

Lake Winnebago unmonitored area

Fox River direct drainage area

Gaging stations 

EXPLANATION

Lake Poygan

Lake Butte

 des Morts

Lake

Winneconne

Lake Winnebago

Wolf

River

Fond du Lac

New London

Berlin

Upper Fox River

Figure 6. Monitored and unmonitored areas of the watershed of 

the Winnebago Pool Lakes, Wisconsin. Gaging stations are identified 

on the figure.
Table 7. Calculation of Soil and Water Assessment Tool ratios used to extraplolate measured flows and phosphorus loads at selected sites in th

Pool Basin to unmonitored areas in the basin. All flows and phosphorus loads are average annual totals for the specified period simulated with S2011 (The Cadmus Group, 2018).[SWAT, Soil and Water Assessment Tool; --, not available]

Flow/load 

parameter

Wolf River at 

New London

Entire Poygan 

and 

Winneconne 

basin

Fox River at 

Berlin

Entire Butte des 

Morts basin

Nearshore 

between Butte 

and Winnebago

Fond du Lac 

River at 

Fond du Lac

nears

cont

Fo

Streamflow, in millions of cubic meters

May–September

Flow 693 1,180 455 524 16 60 

SWAT-flow ratios -- 1.700 -- 1.152 -- -- 

Annual

Flow 1,600 2,710 1,030 1,180 34 106 

SWAT-flow ratios -- 1.700 -- 1.141 -- -- 

Phosphorus loading, in kilograms

May–September

Total load 63,900 108,000 45,100 51,600 4,560 10,600 

Point source load -- 2,260 -- 839 -- -- Nonpoint load -- 106,000 -- 50,700 -- -- SWAT-load ratios -- 1.658 -- 1.125 -- -- 

Annual

Total load 115,000 194,000 71,200 82,000 10,500 20,600 

Point source load -- 5,390 -- 2,000 -- -- Nonpoint load -- 188,000 -- 80,000 -- -- SWAT-load ratios -- 1.642 -- 1.124 -- -- 
Phosphorus Inputs to the Winnebago Pool Lakes 23

Water Budget Summary

While developing the water budget for Lake Winnebago, 

it was noticed that the measured and estimated volumes of the 

lake deviated from one another starting in October 2013. Moving the primary equipment used to estimate flow at the Fox 

River at Appleton may have caused this deviation (R. Waschbusch, U.S. Geological Survey, 2017, oral commun.); therefore, estimated outflows from the lake after September 2013 

were increased by 9 percent, which resulted in equation 10 

reproducing the changes in the volume of Lake Winnebago 

throughout WY2009–14 without any long-term bias (fig. 5). 

The discrepancy between measured and estimated water volume in 2009–10 may have been caused by using rainfall from 

only one location in the basin and using similar evaporation 

rates in all years.

During WY2009–14, the Fox River was the largest 

contributor of water to Lake Winnebago, contributing about 

84 percent of its total water input for May–September and 

85 percent for the entire year (table 6). Direct precipitation 

represented about 9–12 percent of the total input, and the 

Fond du Lac River and nearshore areas each represented 

about 2–3 percent of the total input. Based on these input 

rates during May–September, the residence time (time 

required for water entering the lake to completely replace its 

volume) ranged from 0.37 years during wet periods (2014) 

to 0.78 years during dry periods (2009), with an average of 

0.47 years during May–September 2009–11.

On an annual basis, the total output of water from the 

lake was similar to the total input in all years, which resulted 

in little change in storage from the beginning to the end of 

each water year. On average, about 81–90 percent of the total 

water leaving the lake left through its outlets to the Fox River 

at Neenah Menasha. Evaporation represented between about 

11 percent of water loss during the entire year and 17–18 percent during May–September (table 6).

Phosphorus Inputs to the Winnebago 

Pool Lakes

To describe where the P entering each of the Winnebago 

Pool Lakes originates from and how much may be controllable, detailed annual and May–September P budgets were 

computed for WY2009–14 for Lake Winnebago, and then this 

information was used to develop detailed P budgets for all 

four Pool Lakes for WY2009–11. A shorter period was used 

for all four lakes because information for some of the source 

components, primarily transport from the upstream lakes, were 

not available for Lake Winneconne and Lake Butte des Morts 

for the entire period. The P budget for a period of interest is 

described in equation 5. From equation 5, changes in TP concentrations in a lake can be estimated by dividing its total net 

daily P input by its volume.

Nonpoint Surface-Water Inputs

Measured tributary TP concentrations and loading.—

TP concentrations were measured at five riverine sites in the 

Winnebago Pool watershed (fig. 1). TP concentrations at all 

sites in the watershed demonstrated distinct seasonality; highest concentrations in the rivers occurred around July of each 

year, which is a little before maximum concentrations were 

measured in the lakes (late September) (fig. 7). This seasonality resulted in the May–September average volumetrically 

weighted (VW) concentrations (total P load divided by total 

flow) being higher than the annual averages (table 5), and 

above the phosphorus criterion of 0.075 mg/L for wadeable 

streams (upstream sites) and similar to the 0.100 mg/L criterion 

for nonwadeable rivers (for the downstream Fox River sites) 

in Wisconsin (Wisconsin Department of Natural Resources, 

2017a). Highest TP concentrations were measured in the Fond 

du Lac River, followed by the Fox River at Berlin and the Wolf 

River at New London. The relative magnitude in concentrations was related directly to the amount of agriculture in their 

basins (table 2). In general, TP concentrations measured in the 

Fox River at Oshkosh entering Lake Winnebago, measured 

within the lake, and measured in the Fox River at Neenah 

Menasha leaving the lake were all similar (fig. 7).

Total annual and seasonal (May–September) P loads and 

yields for the five monitored river sites are given in table 5. 

The annual yields from each subbasin were directly related 

to the amount of agriculture in their basins (table 2); highest 

yields (about 40 kilograms per square kilometer [kg/km2]) 

were from the Fond du Lac River that has the most agriculture in its basin, moderate yields were from the Fox River at 

Berlin (about 25 kg/km2), and lowest yields (about 19 kg/km2) 

were from the Wolf River and New London that has the least 

agriculture in its basin. Annual yields immediately upstream 

and downstream from Lake Winnebago (about 19–22 kg/km2) 

were lower than from most of the sites upstream in the basin, 

which indicates part of the P was deposited in the lakes.

The Fox River at Oshkosh was the largest tributary 

input into Lake Winnebago, contributing, on average, about 

300,000 kilograms per year (kg/yr) (tables 5 and 8). Slightly 

more P left Lake Winnebago through the Fox River at Neenah 

Menasha over the entire year than entered through the Fox 

River at Oshkosh; however, inputs from the Fox River at Oshkosh were similar to those leaving the Fox River at Neenah 

Menasha during May–September.

Total nonpoint watershed loading.—Either drainage-area 

ratios or SWAT-load ratios were used to extrapolate the measured P loads at the upstream sites to the total nonpoint watershed P loads (not including input from point sources) into each 

lake for WY2009–11 (table 9). SWAT-load ratios were based 

on the total nonpoint P load to a lake estimated with SWAT 

for WY2009–11 divided by the total P load estimated at an 

upstream gaging station with SWAT for the same period (The 

Cadmus Group, 2018). For May–September P loads, a SWATload ratio of 1.658 was used for extrapolating P load from the 

Wolf River at New London to the total nonpoint surface-water 
24 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

Lake Winnebago Inlet—Fox River at Oshkosh Outlet—Fox River at Neenah Menasha

EXPLANATION

Date

01/09 05/09 09/09 01/10 05/10 09/10 01/11 05/11 09/11

Total phosphorus concentration, in milligrams per liter

0

0.05

0.10

0.15

0.20

0.25

Wolf River at New London Fox River at Berlin Fond du Lac River at Fond du Lac Lake Winnebago

EXPLANATION

0

0.10

0.20

0.30

0.40

0.50

0.60

Date

01/09 05/09 09/09 01/10 05/10 09/10 01/11 05/11 09/11

IP-094896-fig 07 Total phosphorus concentration, in milligrams per liter

Figure 7. Total phosphorus concentrations measured in rivers throughout the Winnebago Pool watershed and in Lake Winnebago, 

Wisconsin, 2009–11.
Table 8. Summary of the phosphorus-budget components for Lake Winnebago, Wisconsin, water years 2009–14.

[NE, not estimated]

Year Fox River Fond du Lac River Nearshore Groundwater Precipitation Internal loading diffusion Other internal sources Septic Point sources1 Tota

Annual phosphorus loading

Phosphorus loading, in kilograms

2009 216,000 17,400 5,150 629 13,600 NE NE 158 8,240 26

2010 272,000 28,000 8,300 629 19,800 NE NE 158 8,240 33

2011 390,000 16,800 4,970 629 14,200 NE NE 158 8,240 43

2012 247,000 11,100 3,300 631 16,700 NE NE 158 8,260 28

2013 298,000 15,100 4,480 629 18,000 NE NE 158 8,240 34

2014 461,000 16,400 4,872 629 20,600 NE NE 158 8,240 51

Average 2009–14 314,000 17,500 5,179 629 17,200 NE NE 158 8,240 36

Average 2009–11 293,000 20,700 6,141 629 15,900 NE NE 158 8,240 34

Average 2009–13 285,000 17,700 5,240 629 16,500 NE NE 158 8,240 33

Percentage of total input

2009–14 86.5 4.8 1.4 0.2 4.7 NE NE 0.0 2.3 

2009–11 85.0 6.0 1.8 0.2 4.6 NE NE 0.0 2.4 2009–13 85.5 5.3 1.6 0.2 4.9 NE NE 0.0 2.5 

May–September phosphorus loading

Phosphorus loading, in kilograms

2009 97,900 4,970 1,470 264 6,490 33,900 204,000 66 3,450 252010 186,000 17,900 5,310 264 13,400 33,900 204,000 66 3,450 462011 200,000 6,780 2,010 264 7,240 33,900 204,000 66 3,450 452012 124,000 3,290 976 264 8,730 33,900 204,000 66 3,450 372013 158,000 5,720 1,690 264 8,450 33,900 204,000 66 3,450 412014 245,000 9,800 2,900 264 11,200 33,900 204,000 66 3,450 51

Average 2009–14 168,000 8,080 2,400 264 9,250 33,900 204,000 66 3,450 42Average 2009–11 161,000 9,890 2,930 264 9,040 33,900 204,000 66 3,450 42

Average 2009–13 153,000 7,740 2,290 264 8,860 33,900 204,000 66 3,450 41

Percentage of total input

2009–14 39.2 1.9 0.6 0.1 2.2 7.9 47.4 0.0 0.8 

2009–11 38.0 2.3 0.7 0.1 2.1 8.0 48.0 0.0 0.8 2009–13 37.1 1.9 0.6 0.1 2.1 8.2 49.2 0.0 0.8 

1Point sources inputs were estimated based on a daily average input for 2011 for all periods.2Percentage of the total input of phosphorus to Lake Winnebago.
Table 9. Summary of the total flow and phosphorus-budget components for the Winnebago Pool Lakes, Wisconsin, water years 2009–11.

[P, phosphorus; Mm3, million cubic meter; p, phosphorus; kg, kilogram. Bold text refers to the total external loading and total input to each of the Winnebago Pool Lakes]

Source

Lake Poygan Lake Winneconne Lake Butte des Morts 

Flow

(Mm3)

Total P

(kg)

Total P

(percent)

Flow

(Mm3)

Total P

(kg)

Total P

(percent)

Flow

(Mm3)

Total P

(kg)

Total P

(percent)

Flow

(Mm3)

Total annual input

Upstream Pool Lakes 0 0 0.0 2,790 220,000 97.3 2,790 209,000 65.2 3,960 

Upstream point sources 0 0 0.0 0 5,270 2.3 0 5,390 1.7 17 Nonpoint watershed 2,780 205,000 96.6 0 0 0.0 1,270 103,000 32.1 260 

Precipitation 48 1,740 0.8 16 573 0.3 29 1,060 0.3 437 Groundwater 2 106 0.0 1 53 0.0 3 159 0.0 12 Direct Point Sources 13 5,270 2.5 0 117 0.1 3 2,000 0.6 10 Septic 0.0 27 0.0 0 13 0.0 0 25 0.0 0 Total external loading 2,850 212,000 100.0 2,800 226,000 100.0 4,100 321,000 100.0 4,700 

May–September input

Upstream Pool Lakes 0 0 0.0 1,220 107,000 94.6 1,220.0 100,000 51.3 1,800 

Upstream pointsources 0 0 0.0 0 2,210 1.9 0.0 2,260 1.2 7 Nonpoint watershed 1,220 118,000 83.2 0 0 0.0 568.0 64,300 32.9 91 Precipitation 27 987 0.7 9 324 0.3 16.6 603 0.3 248 Groundwater 1 44 0.0 0 22 0.0 1.3 67 0.0 5 

Point sources 5 2,210 1.6 0 49 0.0 1.2 838 0.4 4 Septic 0 11 0.0 0 6 0.0 0.0 11 0.0 0 Total external loading 1,250 121,000 85.5 1,230 110,000 96.9 1,810.0 169,000 86.1 2,150 

Internal loading1 0 20,400 14.5 0 3,500 3.1 0.0 27,100 13.9 0 

Total input 1,250 141,000 100.0 1,230 113,000 100.0 1,810.0 196,000 100.0 2,150 

1Internal loading estimates obtained from BATHTUB modeling.
Phosphorus Inputs to the Winnebago Pool Lakes 27

P load into Lake Poygan, and 1.125 was used for extrapolating the P load at the Fox River at Berlin to the total nonpoint 

load into Lake Butte des Morts (table 7). A ratio of 0.369 was 

used for extrapolating the P load measured at the Fond du Lac 

River site to the ungaged nearshore P load to Lake Winnebago. 

This value was based on the SWAT estimated nonpoint P 

load for the nearshore area (3,650 kg; table 7) divided by the 

total load for the Fond du Lac River (9,890 kg; table 8). For 

annual loads, a SWAT ratio of 1.642 was used for extrapolating measured P load at the Wolf River at New London to the 

total nonpoint surface-water P load into Lake Poygan, 1.124 

was used for extrapolating the P load at the Fox River at 

Berlin to the total P load into Lake Butte des Morts (table 7). 

A ratio of 0.296 was used for extrapolating the annual P load 

for the Fond du Lac River (20,700 kg; table 8) to the ungaged 

nearshore P load to Lake Winnebago from SWAT (6,140 kg; 

table 7). Total point sources of P above each of the monitored sites only represented 4.1 to 6.2 percent of the total P 

load if 100 percent of the point source contributions were 

delivered to the monitored location; therefore, these inputs 

were not included in this extrapolation process. To estimate 

the total P loads from the entire Fond du Lac River Basin, a 

1.011 drainage-area ratio was applied to the load measured at 

the upstream gage.

The total nonpoint surface-water P loads to Lake Winnebago from the Fond du Lac River and the remaining 

nearshore areas are given in table 8, and the total nonpoint 

surface-water P loads to all four lakes are given in table 9.

Highest nonpoint watershed P loading into the Pool Lakes 

was from the Wolf River into Lake Poygan (table 9; fig. 8), 

even though the Wolf River had relatively low TP concentrations (table 5). The second highest tributary input came from 

the Fox River into Lake Butte des Morts. Nonpoint tributary 

loading to Lake Winnebago was relatively low even though 

the Fond du Lac River had highest TP concentrations (table 5) 

because most of surface-water loading to Lake Winnebago 

comes from the upstream lakes. The relatively low loads from 

the Fond du Lac River were because of its small drainage area 

and low flow volumes (table 5). The area directly around Lake 

Winnebago had low P loads (based on SWAT simulations) 

because of low estimated TP concentrations. No nonpoint 

watershed input was estimated into Lake Winneconne.

Precipitation

Atmospheric input of P to the Pool Lakes was determined 

from the volume of precipitation on surface of each lake and 

a constant P concentration of 0.036 mg/L. This concentration was obtained from the total precipitation volume and 

an annual deposition rate of 0.3 kilogram per hectare per 

year, which was applied to Wisconsin lakes by Panuska and 

Kreider (2003). This resulted in about 16,000 kg/yr to Lake 

Winnebago, but it varied from 13,600 kg/yr in WY2009 to 

20,600 kg/yr in WY2014 (tables 8 and 9; fig. 8).

Groundwater

Input of P from natural groundwater inflow and septic 

systems were estimated separately. The total P inputs from natural groundwater inflows were computed from the estimated 

flows from a regional groundwater-flow model for the Lake 

Michigan Basin (Feinstein and others, 2010) and an assumed P 

concentration of 0.053 mg/L, which was based on concentrations measured monthly for 2 years in several shallow piezometers around the periphery of Nagawicka Lake (about 100 km 

south of Lake Winnebago) (Robertson and others, 2007). This 

resulted in a total input of 629 kg/yr of P from groundwater to 

Lake Winnebago, 159 kg/yr to Lake Butte des Morts, 106 kg/

yr to Lake Poygan, and 53 kg/yr to Lake Winneconne (tables 8 

and 9; fig. 8).

Septic Systems

P input from near-lake septic systems (M) was estimated 

separately from background groundwater inflow using an 

export coefficient (Es), soil retention coefficient (SR=0.7), and 

the number of people using septic systems around each lake 

each year (capita years) using equation 11 (Reckhow and others, 1980):

 M = Es × (number of capita years) × (1 − SR), (11)

where

Es is input of P per capita per year (0.68 kg; Garn 

and others, 1996).

The number of full-time and seasonal residences with 

near-lake septic systems (properties adjacent to the lakes) 

in 2011 were obtained from the East Central Regional Planning Commission (E. Fowle, written commun., 2013). It 

was assumed that seasonal residences used septic systems 

3 months of the year, and full-time and seasonal residences 

each had three occupants. The number of capita years was 

then calculated by multiplying the number of residences by the 

number of persons per household by the fraction of the year 

occupied.

In 2011, there were 281 full-time residences and 336 seasonal residences using near-lake septic systems around the 

Pool Lakes, which equated to a total of about 1,096 capita 

years (table 10). Therefore, the total P load to the Pool Lakes 

contributed by septic inputs was estimated to be about 224 kg/

yr and 158 kg/yr input into Lake Winnebago (table 10; fig. 8).

Point Sources

Inputs of P from point sources throughout the basin during WY2009–13 were obtained from the WDNR (J. Schmidt, 

written commun., 2014). Only point sources downstream 

from the monitored gages were included in the summaries in 

tables 8 and 9. To estimate the total point source contributions 
28 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin Phosphorus input, in kilograms

100,000

200,000

300,000

400,000

0

500,000

Location

Lake Poygan Lake Winneconne Lake Butte des Morts Lake Winnebago

May to September phosphorus input

Phosphorus input, in kilograms

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

Annual phosphorus input

Nonpoint watershed

Direct point sources

Internal loading Groundwater

Septic

Upstream point sources Upstream pool lakes

Precipitation

EXPLANATION

Figure 8. Average annual and average May–September phosphorus inputs into the Winnebago Pool Lakes, 

Wisconsin, by source, water years 2009–11. Inputs from groundwater and septic systems are not able to be displayed 

because of their relatively small contributions.
Table 10. Phosphorus input from septic systems into the Winnebago Pool Lakes, Wisconsin, 2011.

[ES, kilogram input of phosphorus per capita per year; SR, soil retention fraction; kg/yr, kilogram per year. Bold type indicates total values.]

Pool ES SR

Full-time residences Seasonal residences

Number Residents per unit Fraction of year occupied Number Residents per unit Fraction of year occupied

Lake Poygan 0.68 0.7 30 3 1 54 3 0.25 

Lake Winneconne 0.68 0.7 17 3 1 21 3 0.25 

Lake Butte des Morts 0.68 0.7 35 3 1 26 3 0.25 

Lake Winnebago 0.68 0.7 200 3 1 234 3 0.25 

Total 0.68 0.7 281 3 1 336 3 0.25 
30 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

to each lake (table 9), the point sources were divided into two 

groups: those in the direct drainage area of a specific lake 

(direct point sources), and point sources that contribute to 

upstream Pool Lakes in their basins and could affect their WQ. 

For example, the upstream point sources for Lake Winnebago 

includes all the point sources to the other Upper Pool Lakes 

and those from the city of Oshkosh that is upstream from the 

Fox River at Oshkosh gage. In estimating the contributions 

from upstream point sources, it is assumed that point sources 

above the monitored sites in the basin (upstream from the 

Wolf River at New London, Fox River at Berlin, and Fond 

du Lac River at Fond du Lac) were insignificant (they were, 

however, included in the gaged loads), and it is assumed that 

100 percent of the P load from point sources below the monitored sites reached the lake and were then completely passed 

through the lakes. Summing the P load from point sources and 

upstream point sources provides an indication of the maximum 

potential point source contribution to a lake. The direct point 

sources to Lake Winnebago input was 8,240 kg/yr, and point 

sources upstream from the Fox River at Oshkosh may contribute about an additional 17,200 kg/yr (table 9), totaling about 

25,400 kg/yr (fig. 8).

Upstream Pool Lakes

In a chain of lakes, such as the Winnebago Pool, much 

of P input into the downstream lakes may come from water 

released from the adjacent upstream lake. To estimate the 

amount of P transported downstream from each lake, the 

flow volume leaving the adjacent upstream lake and the TP 

concentration of that water are needed. This was only directly 

measured for Lake Winnebago at the Fox River at Oshkosh. 

For upstream P loading to Lake Winneconne, the flow from 

Lake Poygan was assumed to be equal to tributary input to 

Lake Poygan plus its input from groundwater (that is, it is 

assumed that precipitation equals evaporation), and the TP 

concentration was set equal to that measured in Lake Poygan 

(for estimating May–September loads) or estimated from historical measurements throughout the year in Lake Poygan (for 

estimating annual loads). To estimate the upstream P loading 

into Lake Butte des Morts, the flow from Lake Winneconne 

was assumed to equal the total upstream flow into Lake Poygan plus its groundwater input, and the TP concentration was 

set equal to that measured (for estimating May–September 

loads) or estimated throughout the year in Lake Winneconne 

(for estimating annual loads). The upstream P loading into 

Lake Winnebago was measured at the Fox River at Oshkosh.

The total upstream P input to Lake Winneconne was 

220,000 kg/yr (table 9). The total upstream P input to Lake 

Butte des Morts was slightly less than this (209,000 kg/yr) 

because the TP concentration in Lake Winneconne was a little 

less than that in Lake Poygan. The total upstream P input into 

Lake Winnebago was 276,000 kg/yr (fig. 8).

Surface-Water Outflow

Phosphorus is discharged out of Lake Winnebago into 

the Fox River, estimated at Neenah Menasha. Daily P loads 

into the Fox River at Neenah Menasha were computed using 

daily TP concentrations linearly interpolated from about 

monthly measured concentrations. Total annual P output from 

Lake Winnebago ranged from 229,000 kg in WY2009 to 

481,000 kg in WY2014 (table 8). The average annual P output 

from Lake Winnebago for WY2009–14 was 346,000 kg and 

185,000 kg during May through September.

Release of Phosphorus from Lake Sediments

Typically, internal P loading is thought to primarily happen 

as diffusion of P from the bottom sediments, especially when 

anoxic conditions are present. However, in shallow lakes, 

P release from sediment from resuspension of sediments caused 

by strong winds, fish feeding activities, and fish excretion also 

may be important. To estimate internal P loading to the Pool 

Lakes, first the P released from sediments by diffusion was estimated from laboratory P release rates estimated from sediment 

cores collected from each lake, and then the total P released from 

diffusion and all other mechanisms, including wind resuspension 

and fish activity, was computed using a P budget approach for 

Lake Winnebago and various modeling approaches for all four 

Pool Lakes.

Three types of information are needed to estimate the 

amount of P released by diffusion: the area of sediment from 

which P is being released, characteristics of the sediment surface 

(aerobic or anaerobic), and the P release rate. It was assumed that 

P was released only from areas greater than 1 m deep in Lake 

Winnebago (about 517 km2 or about 97 percent of the surface area 

of the lake) because these areas typically accumulate organic sediment. It is important to determine where and how long the sediment interface is anaerobic because P release typically is much 

higher during anaerobic conditions than during aerobic conditions 

(Mortimer, 1941).

Rates of P release from aerobic and anaerobic sediments in 

the Pool Lakes were estimated from 36 sediment cores collected 

from 15 locations in the Pool Lakes (fig. 1) and analyzed by the 

WSLH. In Lake Winnebago, aerobic release rates ranged from 

0.00 to 1.49 milligrams per square meter per day (mg/m2/d), with 

an average aerobic release rate of 0.43 mg/m2/d (table 11). In the 

three Upper Pool Lakes, average aerobic release rates ranged 

from 0.48 (Lake Winneconne) to 0.80 mg/m2/d (Lake Poygan). 

The average aerobic release rate for all four lakes was 0.55 mg/

m2/d. In Lake Winnebago, daily anaerobic release rates ranged 

from 1.29 to 2.38 mg/m2/d; the average anaerobic release rate was 

1.78 mg/m2/d. In the Upper Pool Lakes, average anaerobic release 

rates ranged from 1.27 (Lake Winneconne) to 1.41 mg/m2/d (Lake 

Butte des Morts). The average anaerobic release rate based on 

data from Lake Winnebago, Lake Butte des Morts, and Lake Winneconne was 1.49 mg/m2

/d. Anaerobic release rates were about 

three to four times greater than the aerobic release rates, and the 

release rates were comparable among lakes.
Table 11. Phosphorus release rates in the Winnebago Pool Lakes, Wisconsin, August, 2010.

[ID, identification number; mg/m2/d, milligram per square meter per day; --, does not apply]

Lake Core ID Condition

Phosphorus 

release rate

(mg/m2

/d)

Aerobic 

average by 

lake

(mg/m2

/d)

Anaerobic 

average by 

lake

(mg/m2

/d)

Winnebago 1A Aerobic 0.25 -- --

Winnebago 1B Aerobic 1.21 -- --

Winnebago 2A Aerobic 0.20 -- --

Winnebago 2B Aerobic 0.19 -- --

Winnebago 3A Aerobic 0.39 -- --

Winnebago 3B Aerobic 0.31 -- --

Winnebago 4A Aerobic 0.10 -- --

Winnebago 4B Aerobic 0.05 -- --

Winnebago 5A Aerobic 0.58 -- --

Winnebago 5B Aerobic 1.49 -- --

Winnebago 6A Aerobic 0.37 -- --

Winnebago 6B Aerobic 0.00 0.43 --

Winnebago 2C Anaerobic 1.88 -- --

Winnebago 2D Anaerobic 2.02 -- --

Winnebago 4C Anaerobic 1.29 -- --

Winnebago 4D Anaerobic 1.79 -- --

Winnebago 6C Anaerobic 2.38 -- --

Winnebago 6D Anaerobic 1.34 -- 1.78

Butte des Morts B1–A Aerobic 0.80 -- --

Butte des Morts B2–A Aerobic 0.47 -- --

Butte des Morts B3–A Aerobic 0.45 -- --

Butte des Morts B3–B Aerobic 0.48 -- --

Butte des Morts B4–A Aerobic 0.32 0.50 --

Butte des Morts B1–B Anaerobic 1.05 -- --

Butte des Morts B2–B Anaerobic 1.16 -- --

Butte des Morts B2–C Anaerobic 1.60 -- --

Butte des Morts B3–C Anaerobic 1.60 -- --

Butte des Morts B4–B Anaerobic 1.63 -- 1.41

Winneconne W1–A Aerobic 0.43 -- --

Winneconne W1–B Aerobic 0.64 -- --

Winneconne W2–A Aerobic 0.37 0.48 --

Winneconne W2–B Anaerobic 1.27 -- 1.27

Poygan P1–A Aerobic 1.35 -- --

Poygan P2-A Aerobic 0.69 -- --

Poygan P2–B Aerobic 0.53 -- --

Poygan P3–A Aerobic 0.61 0.80 --

Overall average of lakes -- -- -- 0.55 1.49

Phosphorus Inputs to the Winnebago Pool Lakes 31
32 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

Based on data collected by the continuous recording 

sensors placed below the buoy on Lake Winnebago (fig. 1), 

DO rarely dropped below 2 mg/L near the sediment interface; therefore, only aerobic release rates were applied from 

May through September in Lake Winnebago. It is believed 

that aerobic conditions existed in the other three Upper Pool 

Lakes; therefore, only aerobic rates also were applied to each 

of them.

With an average aerobic release rate from the cores in 

Lake Winnebago applied from May 1 through September 30, 

the estimated amount of P released from diffusion from Lake 

Winnebago sediments was 33,900 kg (table 8). The amount of 

P released from diffusion before May 1 and after September 30 

is expected to be low because release rates decrease when 

the water temperature is cool during spring, fall, and winter 

(James and Barko, 2004). In addition, during nonsummer 

months, it is expected that sedimentation of P would dominate 

over any diffusion of P from the sediments.

Accuracy of the Phosphorus Budget and Total 

Sediment P Release

To determine the accuracy of the initial P budget for Lake 

Winnebago, and whether additional sources of P might be 

missing from the budget (primarily additional P release from 

the sediments), the estimated changes in TP concentrations in 

Lake Winnebago with equation 5 (computed by dividing the 

daily estimated P mass in the lake by the corresponding daily 

lake volume) were compared with TP concentrations measured 

in or just downstream of Lake Winnebago during WY2009–14 

(fig. 9). Equation 5 was applied starting on the closest date 

prior to May 1 of each year having a measured in-lake TP concentration. Initial TP concentrations were obtained as part of 

routine WDNR monitoring in 2009 through 2011, or from the 

outlet of the lake in 2012 through 2014. Because only limited 

sampling was done in the lake in 2012–14, additional WQ data 

collected at the outlet of the lake (assuming they represented 

TP concentrations in the lake) also were compared to the estimated P concentrations in figure 9. Since all the other terms in 

equation 5 could be accurately estimated, especially the major 

external P contributors, it is believed that any consistent 

discrepancy in measured and estimated TP concentrations in 

Lake Winnebago was because the P release on the basis of 

only diffusion was inadequate at describing the total net sediment P release from the bottom sediments.

Estimated in-lake TP concentrations in Lake Winnebago from about May 1 through September 30 for 2009–14, 

computed using equation 5 with sediment P release rates 

estimated on the basis of internal P loading only from diffusion from aerobic conditions, were consistently much less than 

those measured in the lake (fig. 9). The underestimation in TP 

concentrations indicate that although the TP concentrations in 

the Fox River at Oshkosh, which is the primary input to the 

lake, were close to those measured near the center of the lake 

(fig. 7), the contributions from all the defined P sources were 

not sufficient to cause the observed increase in in-lake TP 

concentrations. This indicates that sources of P in the P budget 

were underestimated or missing, most likely associated with 

additional internal P loading. To estimate this additional internal loading, internal P loading was increased until the estimated TP concentrations in the lake matched those measured 

during May through September in WY2009–14. To approximate the measured concentrations in the lake (or at its outlet) 

in figure 9, the total internal P loading had to be increased 

from 0.43 to 3.00 mg/m2/d (an increase of 2.57 mg/m2/d), 

which may have been caused by resuspension of bottom 

sediment from wind and fish feeding and excretion. Therefore, total net sediment release from diffusion and other 

internal sources during May through September was about 

238,000 kg/yr (table 8) and seems to be greatly underestimated from laboratory diffusion rates alone (33,900 kg). Part 

of this P from internal loading may be a result of errors in the 

other components of the P budgets; however, given that most 

of the P load is from monitored tributary loading (Fox River 

and Fond du Lac River) and input from precipitation (that 

during the 6-year mass-balance period simulated the water 

level of Lake Winnebago accurately; fig. 5), this estimate of P 

from internal loading should be quite reliable. All of the data 

from the mass balance and estimation of internal P loading 

for Lake Winnebago are available at https://doi.org/10.5066/

P9Y8BE4H (Robertson and Kennedy, 2018)

Summary of the Phosphorus Budgets for the 

Winnebago Pool Lakes

During WY2009–14, the average annual input of P 

from external sources into Lake Winnebago was 363,000 kg. 

Additional P is contributed by the sediments during summer months (a net contribution of about 238,000 kg during 

May–September); however, during nonsummer months a 

similar or slightly larger amount of P is deposited back into 

the sediments of the lake. The largest external source of P to 

Lake Winnebago was from the Fox River, which delivered 

about 87 percent of the total annual external P load (table 8), 

part of which represents upstream point sources. Contributions from direct point sources represent about 2.4 percent of 

the total annual external P load, but upstream point sources 

(including the Oshkosh wastewater treatment plant) could 

represent an additional 5.0 percent of the annual external P 

load (table 9). For the entire year, on average 346,000 kg of 

P were exported out of Lake Winnebago (table 8); therefore, 

there seems to be a small net retention of P into the sediments 

of Lake Winnebago.

During May–September, net internal P loading was 

very important to the P budget for Lake Winnebago because 

most of the P input from internal sources (bottom sediment 

and excretion) is during this time and represents more than 

55 percent of the total P input into Lake Winnebago. Because 

of the large contribution from internal sources during May–

September, all the external sources of P become relatively 
Phosphorus Inputs to the Winnebago Pool Lakes 33

Estimated total phosphorus concentration, with internal loading from diffusion 

and other internal sources

Measured in-lake total phosphorus concentration

Measured lake outlet total phosphorus concentration

Estimated total phosphorus concentration, with internal loading from diffusion

EXPLANATION

2009 2010 2011 2012 2013 2014

Date

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Total phosphorus concentration, in milligrams per liter

Figure 9. Measured and estimated near-surface total phosphorus concentrations in Lake Winnebago, Wisconsin, during 

2009–14 using the mass-balance approach.
34 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

less important: Fox River contributed about 38 percent, 

direct point sources contributed 0.8 percent, and precipitation 

contributed about 2.2 percent of the total P input to the lake 

(table 8).

The relative importance of the various P sources varies 

greatly among lakes and season. For Lake Poygan, the primary 

P source is from the Wolf River (nonpoint watershed), and 

the secondary source during summer is from internal loading (fig. 8). For Lake Winneconne, the primary P source is 

from Lake Poygan (its upstream pool lake). For Lake Butte 

des Morts, the primary source is from Lake Winneconne (its 

upstream pool lake), and the secondary source is from the Fox 

River (nonpoint watershed). For Lake Winnebago, the primary 

source for the entire year is from its upstream pool lakes, but 

for the summer months it is from internal loading. For each of 

the lakes, the importance of internal loading increases when 

only the May–September period is considered.

Simulated Changes in Water Quality in 

Response to Changes in Phosphorus 

Loading

Water-Quality Modeling with BATHTUB

The BATHTUB model was used to estimate the expected 

changes in WQ in the Winnebago Pool Lakes in response to 

changes in P loading. In applying BATHTUB, first the average 

conditions for 2009–11 were used to calibrate the model, and 

then 21 scenarios were simulated with the calibrated model 

(table 12). Flow and P loading information from May–September 2009–11 were used to calibrate BATHTUB because 

this is when the most detailed WQ data were collected in the 

lakes and throughout the watershed. In model calibration, the 

measured daily loads within the basin during 2009–11 were 

extrapolated to the entire basin using SWAT ratios. After 

calibration, Scenario 1 simulated the average watershed conditions for 2009–13 based on full SWAT-estimated loadings 

from the watershed. Results from Scenario 1 are used as base 

conditions for which to compare results from all other scenarios. Nine scenarios (2–10) were used to simulate decreases 

in all P loading except inputs from precipitation and natural 

groundwater by 75, 73, 70, 65, 60, 50, 40, 25, and 10 percent; 

and five scenarios (11–15) simulated increases in all P loading 

except inputs from precipitation and natural groundwater by 

10, 25, 50, 75, and 100 percent. Results from scenarios 1–15 

are used to determine the amount of P load reductions that are 

required for the summer-average TP to reach 0.040 mg/L and 

thus be able to delist each of the lakes.

Scenarios 16–21 were then used to examine the effects of 

specific anthropogenic changes in P loading:

• Scenario 16 simulated the effects of removing all 

anthropogenic P sources, and therefore should represent the best WQ conditions possible in the lakes 

(that is, reference conditions). In this simulation, 

TP concentrations in all tributaries to the lakes were set 

to 0.020 mg/L, which is approximately the estimated 

median reference concentration determined by Robertson and others (2006) for streams in central Wisconsin. 

All inputs from point sources and septic systems were 

eliminated, and internal P loading was reduced by a 

percentage similar to the reduction in all other controllable P sources (78- to 80-percent reduction depending 

on the lake).

• Scenario 17 was used to describe how much of the 

anthropogenic inputs could be added back into the 

system in addition to reference loading (scenario 16) 

and yet maintain summer-average TP concentrations at 

or below 0.040 mg/L. To do this, all the anthropogenic 

sources were systematically added to the reference 

loadings until the summer-average TP concentration just reached 0.040 mg/L. In this process, internal 

P loading was changed by a percentage similar to the 

change in all other controllable P sources from base 

conditions.

• Scenario 18 simulated the effects of what would happen if all the tributaries were to reach TP concentrations similar to their P criterion of 0.075 mg/L for 

wadeable streams in Wisconsin (Wisconsin Department of Natural Resources, 2017a). Internal P loading 

was reduced by a percentage similar to the reduction 

in all other controllable P sources (18- to 26-percent 

reduction depending on the lake).

• Scenario 19 simulated the effects of removing inputs 

from all point sources throughout the Winnebago Pool 

basin. Internal P loading was reduced by a percentage similar to the reduction in all other controllable P 

sources (2- to 6-percent reduction depending on the 

lake).

• Scenario 20 simulated the effects of reducing all P 

sources, except precipitation and natural groundwater, 

by 73 percent (this percentage reduction was determined to be the reduction in loading required for Lake 

Winnebago to reach 0.040 mg/L), while maintaining 

internal P loading similar to that estimated during 

base conditions. The WQ from this simulation is what 

would be expected immediately after a 73-percent 

reduction in external P loading, and before internal P 

loading would respond.

• Scenario 21 simulated the effects of only removing all 

the P contributed by internal loading, while keeping all 

other inputs similar to base conditions. This simulation 

examined the effects of internal P loading independently of all other changes.
Table 12. BATHTUB simulation results. Results of changes in phosphorus loading to the Winnebago Pool Lakes, Wisconsin, simulated with BATHTUB 

total phosphorus, chlorophyll a, and Secchi depth in Lake Winnebago. Percent changes in the total phosphorus load, including inputs from internal loain only potentially controllable sources (i.e., inputs from precipitation and groundwater were unchanged). All changes in internal phosphorus loading wchanges in all controllable sources. Simulations were also performed with an additional 25-percent reduction in internal loading.[P, phosphorus; kg, kilograms; TP, total phosphorus; conc., concentration; mg/L, milligram per liter; μg/L, microgram per liter; m, meter; —, does not apply; RD, results dependeUpper Pool Lakes. Base conditions for all comparisons are in bold font.]

Scenarios

Change in internal phosphorus loading similar to change in all controllable sources With an addition

in inte

Scenario 

number

May–

September 

P load (kg)

 TP 

conc. 

(mg/L)

Chlorophyll-a

conc. 

(μg/L)

 Secchi 

depth 

(m)

Annual 

P Load 

(kg)

TP 

conc. 

(mg/L)

May–

September 

P load (kg)

TP 

conc

(mg/L

Measured 422,000 0.097 30.5 1.2 573,000 0.097 — — Calibration 422,000 0.097 29.1 1.2 573,000 0.095 — — 

General response corresponding to percentage change in P load

–75 percent 2 116,000 0.037 16.2 2.0 143,000 0.039 99,000 0.033 

–73 percent 3 124,000 0.039 17.0 1.9 155,000 0.041 106,000 0.035 –70 percent 4 136,000 0.042 17.9 1.8 172,000 0.044 117,000 0.037 –65 percent 5 156,000 0.047 19.4 1.7 200,000 0.049 133,000 0.042 

–60 percent 6 176,000 0.052 20.7 1.6 229,000 0.053 150,000 0.046 –50 percent 7 216,000 0.060 22.8 1.5 286,000 0.062 183,000 0.053 –40 percent 8 255,000 0.068 24.6 1.4 344,000 0.070 215,000 0.060 –25 percent 9 313,000 0.079 26.6 1.3 430,000 0.081 264,000 0.070 –10 percent 10 370,000 0.090 28.2 1.2 516,000 0.091 312,000 0.079 

0 percent–Base 1 408,000 0.096 29.0 1.2 573,000 0.097 343,000 0.085 

+10 percent 11 445,000 0.103 29.8 1.2 630,000 0.103 374,000 0.090 

+ 25 percent 12 510,000 0.112 30.7 1.1 716,000 0.112 420,000 0.09

+ 50 percent 13 593,000 0.126 31.9 1.1 859,000 0.125 497,000 0.111 

+ 75 percent 14 685,000 0.139 32.9 1.1 1,000,000 0.138 572,000 0.123 

+ 100 percent 15 775,000 0.152 33.7 1.1 1,150,000 0.150 646,000 0.134 

Specific natural and anthropogenic scenarios

Reference conditions 16 95,000 0.032 14.2 2.2 RD RD 81,363 0.02

Reference +9 percent (and 

+16 percent) anthropogenic sources

17 124,000 0.040 17.0 1.9 RD RD 124,000 0.040 

0.075 mg/L in all tributaries 18 308,000 0.078 26.5 1.3 RD RD 259,000 0.069 

Base with no point sources 19 398,000 0.093 28.6 1.2 RD RD 333,000 0.084 

73-percent reduction, full internal 

loading

20 318,000 0.080 26.8 1.2 RD RD 252,000 0.068 

Base with no internal loading 21 146,000 0.045 18.7 1.7 RD RD 146,000 0.045 
36 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

When BATHTUB is used to simulate the effects of 

changes in external loading, it is usually assumed that internal 

P loading to the lake will either be unaffected or it will eventually come to a new equilibrium with its new external P loading 

with a change directly proportional to the percentage change 

in all nonsediment sources (Robertson and others, 2018). 

Therefore, in all simulations, except those specifically looking 

at the effects of modifying internal P loading (scenarios 20 and 

21), net internal loading was changed by a percentage similar 

to the change in all other external controllable P sources. The 

resulting changes in internal P loading are a little less than 

the total changes in external P loading to the lake because 

inputs form precipitation and groundwater were unchanged. 

This assumption results in net internal P loading reaching 

0 mg/m2/d before total external loading reaches 0 kg; with a 

75-percent reduction in controllable sources, internal P loading 

into Lake Winnebago was estimated to be 0.70 mg/m2/d compared to 0.82 mg/m2

/d if the change in internal P loading was 

based on the percentage of change in all external P loading to 

the lake. Thus, most of the outputs from the BATHTUB simulations should represent conditions in the future when the lake 

sediments come to equilibrium with their external P inputs. It 

is difficult to determine when these simulated changes would 

actually happen with BATHTUB, but this is examined later 

with the Jensen model.

BATHTUB also was used to examine the effects of 

reducing internal P loading at a rate more than that for the 

other P sources to simulate what may happen if additional 

in-lake actions also are done. These may include actions that 

promote macrophyte growth and thus reduce wind induced 

resuspension or that reduce the population of rough fish, such 

as carp and thus reduce sediment resuspension during feeding 

and reduce P input from excretion. To examine the effects of 

reducing internal loading at a rate more than that projected to 

occur to external sources, all 21 scenarios were again simulated but with an additional reduction in the internal P loading to each lake by 25 percent. It is difficult to estimate the 

magnitude of these types of actions that would be required to 

achieve a specific additional P load reduction. The main reason 

for doing these scenarios is to illustrate that substantial in-lake 

management also may be required to meet WQ goals even if 

substantial watershed load reductions are achieved.

Data Requirements

Four types of data are required as input into BATHTUB: 

morphometric data (table 1), hydrologic data (table 9), P loading data (table 9), and WQ data needed to calibrate and verify 

the model (table 3). The BATHTUB model was set up with 

five interconnected lakes: Lake Poygan, Lake Winneconne, 

Lake Butte des Morts, widening of the Fox River, and Lake 

Winnebago. The widening of the Fox River between Lakes 

Butte des Morts and Winnebago was included as an additional 

lake to enable changes to happen between Lakes Butte des 

Morts and Winnebago. Lake Winnebago was treated as one 

well-mixed lake. The period for the hydrologic and P loading 

used in BATHTUB is dependent on the P-turnover ratio (number of times the P mass in the lakes is replaced in a specific 

period). Because of the short residence times of the Upper 

Pool Lakes, flow and P loadings for May through September 

were used as input to BATHTUB, which resulted in a P-turnover ratio of about 2, which is preferred for model calculations 

(Walker, 1996). The relations within BATHTUB simulate WQ 

during the summer growing season; therefore, BATHTUB 

was calibrated to WQ measured from June through September. Because detailed in-lake WQ data for all four lakes were 

only available for 2009–11, average flow and WQ data for 

these years were used to calibrate the relations in BATHTUB. 

The average precipitation and evaporation for May through 

September 2009–11 were 0.468 and 0.714 m, respectively. 

All input data used in the BATHTUB model and results from 

the model are available at https://doi.org/10.5066/P9Y8BE4H

(Robertson and Kennedy, 2018).

Because Lake Winnebago had a relatively long residence 

time compared to the other lakes, the Canfield and Bachmann 

(1981) natural-lake equation, the algorithm selected within 

BATHTUB (eq. 6), also was used with flow and P inputs for 

the full year (table 9) to determine if changing its averaging period affected its simulated response to the changes in P 

loading in scenarios 1–15 (table 12). In this application, total 

P load was set to 573,000 kg (sum of all annual P loads in 

table 8, but with the internal P load estimated with the seasonal 

BATHTUB model), the mean depth (z̄) was set to 4.54 m, and 

residence time (τ) was set to 0.51 year (table 1).

Phosphorus from internal P loading is not typically 

included as a source in BATHTUB, because most empirical 

models already indirectly incorporate this source. Additional 

internal loading, therefore, is typically only added when a lake 

or reservoir has abnormally high internal loading (Walker, 

1996). It was believed that all the Pool Lakes have abnormally 

high internal loading, as was shown for Lake Winnebago 

(table 8; fig. 9); therefore, additional internal P loading was 

considered for each of the Pool Lakes. Internal P loading to 

each of the Pool Lakes was then estimated using BATHTUB 

by adjusting their internal P loading rate until the estimated 

average TP concentrations in each lake matched those measured during 2009–11. The resulting internal P loads for each 

lake were then used to complete their respective May–September P budgets in table 9.

Algorithms and Calibration

When applying BATHTUB, dispersion coefficients can 

be used to describe the upstream exchange of water with 

adjacent lakes or basins. A dispersion coefficient of 0.0 was 

applied between all adjacent basins, which indicates no 

upstream mixing with the adjacent upstream lakes. Almost 

all the algorithms selected in this application of BATHTUB 

were the default algorithms that have been shown to usually 

be appropriate for most lakes and reservoirs (Walker, 1996), 

except the algorithm to simulate changes in TP. The CanfieldBachmann natural lake equation (algorithm 8 in BATHTUB) 
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 37

has worked well in simulating TP concentrations in lakes 

throughout Wisconsin (Robertson and others, 2012, 2018; 

Robertson and Rose, 2008; Juckem and Robertson, 2013); 

therefore, it was used in this application. Chl-a was simulated 

using estimated TP, residence time, and model-estimated light 

limitation (algorithm 2 in BATHTUB). SD was simulated with 

algorithm 1 in BATHTUB, which used estimated Chl-a and 

model-estimated nonalgal turbidity.

With average May–September loading data (flow and TP 

concentrations) from 2009 to 2011 and internal P loading rates 

based on laboratory aerobic release rates, BATHTUB was 

used to simulate the summer-average (June through September) WQ in each lake. The initial simulated (precalibration) 

TP and Chl-a concentrations were consistently less than those 

measured in the lakes, and simulated SDs were greater than to 

those measured (fig. 10). These differences between measured 

and simulated WQ indicate that the total P loads to the lakes 

were likely underestimated when aerobic internal P release 

rates were used to estimate the net internal P loading because 

of it not incorporating inputs from other internal sources; 

therefore, the internal P loading to all Pool Lakes were 

increased until the simulated TP concentrations (postcalibration) matched those measured in 2009–11 (fig. 10). The rates 

of net internal P loading were increased from 0.80 to 2.30 mg/

m2/d in Lake Poygan, increased from 0.48 to 1.20 mg/m2/d 

in Lake Winneconne, increased from 0.50 to 5.00 mg/m2/d in 

Lake Butte des Morts, and increased from 0.43 to 2.80 mg/

m2/d in Lake Winnebago. For Lake Winnebago, the final estimated internal P loading was a little less than that estimated 

with the mass balance approach (3.0 mg/m2/d). The internal 

P loading rates for Lake Butte des Morts were not used to 

completely match measured in-lake concentrations because 

they also were used to try to match downstream P loading 

measured at the Fox River at Oshkosh, which also is computed 

in BATHTUB. During this calibration process, it was not possible to match the TP concentrations in Lake Butte des Morts 

without slightly overestimating the P load entering Lake Winnebago from the Fox River. Therefore, the Fox River segment 

was added to the model and a calibration coefficient (2.0) was 

applied to its TP concentration. This calibration factor reduced 

the TP in the Fox River segment and allowed the model to 

more closely match the P load measured at the Fox River at 

Oshkosh.

Based on the refined internal P loading estimates for all 

four Pool Lakes from BATHTUB, the total May–September 

P budget for each Pool Lake could be completed (table 9; 

fig. 8). During WY2009–11, the average May-September 

P input to Lake Winnebago was 415,000 kg, of which 

187,000 kg came from external sources (45 percent) and 

228,000 kg came from internal loading in the lake (55 percent). During May–September, net internal loading becomes 

much more important for each of the lakes. The importance 

of the net internal P loading varied from 3.1 percent for Lake 

Winneconne, to 13.9 percent for Lake Butte des Morts, to 

14.5 percent for Lake Poygan, and to 55 percent for Lake Winnebago. Although the rate of internal P loading was relatively 

high in the Upper Pool Lakes, its relative importance to their 

total P budgets was less than for Lake Winnebago because of 

the magnitude of the other sources, primarily tributary loading 

and inputs from the adjacent upstream lake. Internal loading 

was omitted from the total annual inputs in table 9 because 

a net loss of P into Lake Winnebago was estimated from its 

annual P budget (table 8), which also was expected in the 

other lakes.

After adjusting the net internal P loading in the TP 

algorithms, the Chl-a algorithms for the Upper Pool Lakes 

in BATHTUB still did not simulate Chl-a well. Therefore, 

calibration coefficients were applied to the Chl-a algorithms 

for Lake Poygan (1.13), Lake Winneconne (1.9), and Lake 

Butte des Morts (2.2). No calibration was required for simulating Chl-a in Lake Winnebago. After adjusting net internal P 

loading in the TP models and calibrating the Chl-a algorithms 

for the Upper Pool Lakes, no calibration was needed for 

simulating SDs. The simulated (precalibration and postcalibration) and measured WQ values for 2009–11 are compared 

in figure 10. After model calibration, BATHTUB accurately 

simulated TP, Chl-a, and SD in all four lakes.

Response in Water Quality to Basinwide 

Changes in Phosphorus Loading

To estimate the expected response in WQ in the Winnebago Pool Lakes to changes in P loading from all potentially 

controllable sources (all inputs except those from precipitation 

and natural groundwater) and to determine the reduction in 

P loading required to each lake to reach a mean summer TP 

of 0.040 mg/L, 15 scenarios (1–15) were simulated with the 

BATHTUB model. Based on these simulations, TP in each 

Pool Lake should have a relatively linear response to changes 

in P loading (fig. 11A; table 12 for Lake Winnebago only). 

The changes in in-lake TP, on a percentage basis, are smaller 

than the changes in external P loading. A 75-percent decrease 

in all potentially controllable P sources into Lake Winnebago, 

which equates to a 72-percent decrease in total P loading from 

all sources, results in a 61-percent decrease in TP in Lake Winnebago; and a 75-percent increase in all potentially controllable P sources, which equates to a 68-percent increase in total 

P loading from all sources, results in a 45-percent increase in 

TP in Lake Winnebago.

Based on the TP response curve for Lake Winnebago, it 

would require a 73-percent reduction in P loading from all its 

potentially controllable sources to reach an average June–September TP concentration less than 0.040 mg/L (the P criterion 

for this lake). Based on the TP response curves for the Upper 

Pool Lakes, a slightly smaller reduction would be required for 

those lakes (about 60 percent) to reach 0.040 mg/L. However, 

if a 60-percent reduction in all potentially controllable sources 

were achieved for the Upper Pool Lakes, then Winnebago 

would not be able to reach 0.040 mg/L. Therefore, a 73-percent reduction in P input is needed from throughout the basin 

for all four Pool Lakes to reach 0.040 mg/L.
38 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

IP-094896-fig10

EXPLANATION

Secchi depth, in meters

Secchi depth

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Lake Poygan Lake Winneconne Lake Butte des Morts Lake Winnebago

Location

0

10

20

30

40

50

60

Chlorophyll-a concentration,

in micrograms per liter

Chlorophyll a

Total phosphorus

Total phosphorus concentration,

in milligrams per liter

0

0.02

0.04

0.06

0.08

0.10

0.12

Figure 10. Measured and simulated (with the BATHTUB model) summer-average near-surface total 

phosphorus concentrations, chlorophyll-a concentrations, and Secchi depths in the Winnebago Pool 

Lakes, Wisconsin.
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 39

–100

–80

–60

–40

–20

0

20

40

60

80

100

Percentage chagne (Lake 

Winnebago)

0.0

0.5

1.0

1.5

2.0

2.5

–100 –75 –50 –25 0 25 50 75 100

Secchi depth, in meters

0

10

20

30

40

50

60

70

Chlorophyll-a concentration, micrograms per liter

–100

–80

–60

–40

–20

0

20

40

60

80

100

120

–100 –75 –50 –25 0 25 50 75 100

Percentage change (Lake Winnebago)

−80

−60

−40

−20

0

20

40

60

80

Percentage change (Lake Winnebago)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Total phosphorus concentration, milligrams per liter

−100 −75 −50 −25 0 25 50 75 100

–100

73-percent reduction

in external loading

with no internal loading

Reference plus 

9 percent

0.075 milligram per 

liter in all tributaries

No point sources

Base with no

internal loading

Reference conditions

73-percent reduction in 

external loading with no interna

R

l loading

eference plus 

9 percent

0.075 milligram per liter in all tributaries

No point sources

Base with no internal loading

Reference conditions

73-percent reduction in 

external loading with no interna

R

l loading

eference plus 

9 percent

0.075 milligram per 

liter in all tributaries

No point sources

Base with no internal loading

Reference conditions

Change in phosphorus loading, in percent

Change in phosphorus loading, in percent

Change in phosphorus loading, in percent

Lake Poygan

Lake Winneconne

Lake Butte des Morts

Lake Winnebago

Lake Winnebago

only—Annual

Lake Winnebago

base conditions

Nutrient criteria

EXPLANATION

A

B

C

Figure 11. Simulated changes in summer-average water quality in the Winnebago Pool Lakes, Wisconsin, in response to various 

phosphorus-loading scenarios (table 12) using the BATHTUB model. A, Total phosphorus. B, Chlorophyll a. C, Secchi depth.
40 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

The Canfield and Bachmann (1981) natural-lake equation, algorithm within BATHTUB (eq. 6,) also was used with 

flow and P inputs into Lake Winnebago for the full year to 

determine if changing its averaging period affected its simulated response to the changes in P loading in scenarios 1–15. 

Equation 6 simulated growing season TP for 2011–13 to be 

0.095 mg/L, close to that measured in the lake: 0.097 mg/L. 

Because of the small discrepancy in measured and simulated 

values, all simulated TP values were increased by 2 percent. 

A similar TP response curve to that obtained with BATHTUB 

using seasonal inputs was obtained for Lake Winnebago when 

equation 6 was used with flow and P inputs for the full year 

(fig. 11; table 12). With a 75-percent reduction in controllable P sources, simulated TP was only 0.002 mg/L more 

than that obtained using seasonal inputs in BATHTUB; and 

with a 100-percent increase in controllable P sources, the 

simulated TP was only 0.002 mg/L less than that estimated 

using seasonal inputs. When annual inputs were considered, a 

74-percent reduction in P loading from all potentially controllable sources to Lake Winnebago was needed for it to 

reach an average June–September TP concentration less than 

0.040 mg/L, which is almost identical to that determined using 

seasonal P inputs. Based on the similarity in these responses, 

similar results would be expected for all other scenarios if 

annual inputs were used; however, the actual response in Lake 

Winnebago depends on changes in the Upper Pool Lakes 

that cannot be simulated using equation 6 independent of the 

Upper Pool Lakes.

Simulated summer-average Chl-a had a nonlinear 

response to a linear change in P loading (fig. 11B; table 12 

for Lake Winnebago). The response in Chl-a was larger (on a 

percentage basis) for decreases in P loading than for similar 

increases in loading. A 75-percent reduction in P loading to 

Lake Winnebago resulted in a 44-percent reduction in Chl-a

(from 29.6 to 16.2 μg/L), whereas a 75-percent increase 

in P loading resulted in an increase of only 13.4 percent. 

A 73-percent decrease in P loading should reduce summeraverage Chl-a in Lake Winnebago to 17.0 μg/L.

Simulated summer-average SDs also were more responsive to decreases in P loading than to increases in P loading 

(fig. 11C; table 12 for Lake Winnebago). When P loading to 

Lake Winnebago was decreased by 75 percent, SD increased 

to 2.0 m (67-percent increase); however, when loading was 

increased by 75 percent, SD decreased to 1.1 m (8-percent 

decrease). A 73-percent decrease in P loading should increase 

summer-average SD in Lake Winnebago to 1.9 m.

Summer-average TSI values indicate that all Winnebago 

Pool Lakes are highly eutrophic (TSI values between 60 and 

70; table 3). Based on the simulations with BATHTUB, if P 

loading could be reduced by 60–75 percent from that measured in 2009–11, WQ in all Pool Lakes should improve, but 

the lakes would still be classified as eutrophic.

Potential Water Quality

To estimate the best potentially achievable WQ in the lakes 

(that is, reference conditions, scenario 16), TP concentrations 

in all the tributaries to the lakes were set to 0.020 mg/L (the 

approximate median reference concentration for streams in central Wisconsin when all agriculture and urban sources of P were 

simulated to be removed from their basins; Robertson and others, 2006), P inputs from point sources and septic systems were 

eliminated, and internal P loading was reduced by a percentage 

similar to the reduction in all the other controllable P sources 

(about an 80-percent reduction in internal P loading for each 

lake). Based on BATHTUB results (fig. 11; table 12 for Lake 

Winnebago), the best possible summer-average WQ should be 

TP concentrations ranging from 0.022–0.024 mg/L in the Upper 

Pool Lakes to 0.032 mg/L in Lake Winnebago; Chl-a concentrations ranging from 10 μg/L in Lake Poygan, to 14 μg/L in Lakes 

Winneconne and Winnebago, and to 19 μg/L in Lake Butte des 

Morts; and SDs ranging from 1.0 m in Lake Butte des Morts, 

to 1.2 m in Lake Poygan and Lake Winneconne, and to 2.2 m 

in Lake Winnebago. These conditions are better than the WQ 

criteria for shallow drainage lakes in Wisconsin (Wisconsin 

Department of Natural Resources, 2017a).

Effects of Specific Phosphorus Reductions from 

the Watershed

To determine how much of the anthropogenic P inputs 

could be added in addition to reference P loading and yet 

maintain summer-average TP concentrations at or below 

0.040 mg/L, all the anthropogenic sources were systematically 

adjusted at similar rates, and internal P loading was adjusted 

at a rate similar to the change in all the other potentially 

controllable P sources. If all TP concentrations in the rivers, 

point sources, and septic systems increase less than 9 percent 

from their reference concentrations (and an associated 71- to 

73-percent reduction in internal P loading from base conditions), the summer-average TP concentration in Lake Winnebago should be just less than 0.040 mg/L. The final results 

of this evaluation are described as scenario 17 (table 12; 

fig. 11).

To determine the potential effects of management strategies in the watershed that are sufficient to reduce the average 

TP concentrations in all the tributaries to the Pool Lakes to the 

current P criterion of 0.075 mg/L (scenario 18), all TP concentrations in the tributaries were set to 0.075 mg/L, and internal 

P loading was reduced by a percentage similar to the change in 

all the other P inputs (18 percent in internal P loading to Lake 

Poygan to 26 percent in Lake Winnebago). With all rivers 

entering at 0.075 mg/L, summer-average WQ should improve: 

TP concentrations should range from 0.071 to 0.077 mg/L 

in the Upper Pool Lakes to 0.078 mg/L in Lake Winnebago; 
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 41

Chl-a concentrations should range from 27 μg/L in Lake 

Winnebago, to 32 μg/L in Lake Poygan, to 36 μg/L in Lake 

Winneconne, and to 48 μg/L in Lake Butte des Morts; and 

SDs should range from 0.7 m in the Upper Pools to 1.3 m in 

Lake Winnebago. These conditions in the Pool Lakes are still 

worse than the WQ criteria defined for shallow drainage lakes 

in Wisconsin (Wisconsin Department of Natural Resources, 

2017a).

Scenario 19 simulated the effects of eliminating all the 

P inputs from point sources downstream from the monitored 

gaging stations. In this scenario, it was initially assumed that 

internal P loading would not change from baseline conditions; therefore, it would represent the immediate effects of 

point source removal. With P from all point sources removed 

(immediately after removing the point sources), summer-average WQ changed little: TP concentrations decreased by about 

0.001 mg/L in all lakes, and little changes in Chl-a concentrations and SDs were measured. If the elimination of point 

sources were assumed to also reduce internal P loading by a 

percentage similar to the reduction in all the other potentially 

controllable P sources (future equilibrium), then a little more 

improvement in WQ was determined for Lake Winnebago, 

but no change was observed for the Upper Pool Lakes. If the 

elimination of P from point sources also fully affected internal loading in Lake Winnebago by a similar percentage, TP 

should decrease from 0.096 to 0.093 mg/L, and Chl-a should 

decrease from 29.0 to 28.6 μg/L, but no change in SD should 

be observed.

Effects of Internal Loading on In-Lake Water 

Quality

To estimate how important internal P loading is to WQ 

in the Pool Lakes, two simulations were done: in scenario 21, 

internal P loading was eliminated from the base simulation; 

and in scenario 20, the reduction in internal P loading was 

eliminated from the 73-percent reduction in P loading (scenario 3 but with no reductions in internal P loading). If the 

internal P loading estimated for 2009–11 could be eliminated 

but external P loading was left unchanged, WQ in all four 

Pool Lakes should greatly improve, especially the WQ in 

Lake Winnebago where the internal P loading was its largest 

source of P during summer (fig. 8). With internal P loading 

eliminated, summer-average TP concentrations should range 

from 0.045 mg/L in Lake Winnebago to 0.070–0.077 mg/L 

in the Upper Pool Lakes; Chl-a concentrations should range 

from 19 μg/L in Lake Winnebago, to 33 μg/L in Lake Poygan, 

to 36 μg/L in Lake Winneconne, and to 47 μg/L in Lake Butte 

des Morts; and SDs should range from 0.6–0.7 m in the Upper 

Pool Lakes to 1.7 m in Lake Winnebago.

Based on results from scenario 3 (73-percent reduction 

in all potentially controllable P sources), TP concentrations 

throughout the Winnebago Pool Lakes should eventually 

decrease to below 0.040 mg/L; however, these changes and the 

other changes in WQ will only be observed after the system 

(internal P loading) comes to equilibrium with its new external 

P loading. Scenario 20 simulates the immediate effects of a 

73-percent reduction in external P sources. In this scenario, 

all external sources were reduced by 73 percent, but internal 

P loading was left unchanged (that is, did not have time to 

equilibrate with its P reduction from the other sources). In the 

years immediately after a 73-percent reduction in all external 

P sources, WQ should improve throughout the system (fig. 11), 

especially in the Upper Pool Lakes where internal P loading 

was a relatively small source (fig. 8). With a 73-percent reduction in all external loading and no change in internal P loading: 

TP concentrations should range from 0.038 mg/L in Lake 

Poygan and Lake Winneconne, to 0.047 mg/L in Butte des 

Morts, and to 0.080 mg/L in Lake Winnebago; Chl-a concentrations should range from 18 to 24 μg/L in Lake Poygan 

and Lake Winneconne, to 27 μg/L in Lake Winnebago, and to 

35 μg/L in Lake Butte des Morts; and SDs should range from 

about 0.5 to 0.7 m in the Upper Pool Lakes to 1.2 m in Lake 

Winnebago. Therefore, large reductions in external P sources 

should result in an almost immediate improvement in WQ, 

especially in lakes where internal P loading is a relatively 

small source, but the internal P loading will delay the full 

effects of the reductions from being observed in the Winnebago Pool Lakes. It is not possible, however, to determine 

how long it will take the Winnebago Pool Lakes to come into 

this new equilibrium with BATHTUB.

BATHTUB was then used to examine the effects of 

reducing the inputs from internal P loading by 25 percent in all 

the scenarios to simulate what may happen if in-lake actions 

also are done in addition to any of the external P input changes 

described in table 12, such as activities to promote macrophyte 

growth that should reduce the wind resuspension or activities 

to reduce the population of rough fish that resuspend bottom 

sediment during feeding and have high P excretion rates.

With a 25-percent reduction in the inputs from internal 

P loading in all of the scenarios, all the simulated response 

curves shown in figure 11 shifted toward better WQ and the 

WQ for each of the individual scenarios improved (fig. 12; 

table 12). The improvements in WQ were larger for Lake 

Winnebago than for the other lakes because internal P loading was relatively more important for Lake Winnebago than 

the other lakes. If internal P loading was reduced by 25 percent, the overall external P load reduction needed for all four 

Pool Lakes to reach 0.040 mg/L decreased from a 73- to a 

67-percent reduction from the loading for base conditions. 

Potentially achievable WQ in Lake Winnebago also improved: 

reference summer-average TP decreased from 0.032 to 

0.028 mg/L, Chl-a decreased from 14.2 to 12.7 μg/L, and a SD 

increased from 2.2 to 2.4 m. The reduction in the inputs from 

internal P loading by 25 percent also increased the amount of 

additional external P loading that could happen above reference conditions and yet maintain a TP concentration in Lake 

Winnebago just below 0.040 mg/L from 9 to 16 percent.
42 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

IP-094896_fig 12

Lake Poygan

Lake Winneconne

Lake Butte des Morts

Lake Winnebago

Lake Winnebago

base conditions

Nutrient criteria

EXPLANATION

–50

0

50

100

0.00 –100

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Total phosphorus concentration, in 

milligrams per liter

−100 −75 −50 −25 0 25 50 75 100

Change in phosphorus loading, in percent

–100

–100

Reference conditions

Percentage change (Lake Winnebago)

–50

0

50

100

150

0

10

20

30

40

50

60

70

–100 –75 –50 –25 0 25 50 75 100

Percentage change (Lake Winnebago)

Chlorophyll-a concentration, in micrograms per liter

Change in phosphorus loading, in percent

Percentage change (Lake Winnebago)

–50

0

50

100

150

0.5

1.0

1.5

2.0

2.5

3.0

–100 –75 –50 –25 0 25 50 75 100

Secchi depth, in meters

Change in phosphorus loading, in percent

0.0

Reference conditions

Reference conditions

73-percent reduction in 

external loading with no

internal loading

Reference plus 16 percent

0.075 milligram per liter

in all tributaries

No point sources

Base with no

internal loading

A

B

C

73-percent reduction in 

external loading with no internal loading

Reference plus 16 percent

0.075 milligram per liter

in all tributaries

No point sources

Base with no

internal loading

73-percent reduction in 

external loading with no internal loading

Reference plus 16 percent

0.075 milligram per liter

in all tributaries

No point sources

Base with no internal loading

Figure 12. Simulated changes in summer-average water quality in the Winnebago Pool Lakes, Wisconsin, in response to various 

phosphorus-loading scenarios (table 12), with internal loading reduced by 25 percent using the BATHTUB model. A, Total phosphorus. 

B, Chlorophyll a. C, Secchi depth.
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 43

Water-Quality Modeling with the Jensen Model

Results from BATHTUB simulations were used to 

describe the changes in summer-average WQ that should 

happen in the future when the internal P loading in the lakes 

comes into a new equilibrium with the changes in external 

P inputs; however, BATHTUB does not describe the transient 

changes in WQ after the changes in external P inputs or the 

seasonal changes that happen throughout the year. Results 

from the Jensen model (Jensen and others, 2006) can be used 

to describe these shorter-term changes in WQ and the temporal changes in internal P loading. In this study, the daily 

P loadings and measured TP concentrations in the lakes and 

their outlets during WY2009–13 (extrapolated using SWAT 

ratios based on annual average flows and loads) were used to 

calibrate two independent Jensen models: one for the Upper 

Pool Lakes (Lake Poygan, Lake Winneconne, and Lake 

Butte des Morts collectively) terminating at the Fox River at 

Oshkosh, and one for Lake Winnebago terminating in the lake. 

Then, output from the Upper Pool Lakes Jensen model was 

used as input to the Lake Winnebago Jensen model to create 

one linked Jensen model for the entire Pool terminating in 

Lake Winnebago, but simulating changes at the downstream 

end of the three Upper Pool Lakes and in Lake Winnebago. 

Calibrations were based on WY2009–13 for the independent 

models, and the results are shown for the linked Jensen model. 

After calibration with extrapolated measured loads from the 

watershed, 18 P loading scenarios (1–J through 18–J) were 

simulated with the calibrated linked Jensen model (summarized in table 13). Scenario 1–J was used to simulate WQ in 

the lakes given the watershed conditions during WY2009–13 

but based on loadings from full SWAT estimations, which 

provides base conditions for which to compare results from 

all other Jensen simulations. Then, 13 scenarios were used 

to examine the effects of changes in basinwide inputs: 8 scenarios (2–J through 9–J) simulated the effects of decreases 

in all P loading (except inputs from precipitation and natural 

groundwater that remained unchanged) by 80, 75, 70, 69, 65, 

50, 25, and 10 percent, and 5 scenarios (10–J through 14–J) 

simulated the effects of increases in all P loading by 10, 25, 

50, 75, and 100 percent. Results from these simulations were 

again used to determine the reduction in P loading required 

for summer-average TP concentrations in the lakes to decrease 

below 0.040 mg/L. Scenario 15–J (similar to scenario 16 

with the BATHTUB model) simulated the effects of removing all anthropogenic P sources and, therefore, represents the 

best conditions possible in the lakes (that is, reference conditions). In scenario 15–J, TP concentrations in all tributaries to 

the lake were set to 0.020 mg/L, and all P inputs from point 

sources and septic systems were eliminated. Scenario 16–J 

was then used to demonstrate how much anthropogenic input 

could be added in addition to reference P loadings and yet 

maintain a summer-average TP at or below 0.040 mg/L (similar to scenario 17 with BATHTUB). Scenarios 17–J and 18–J 

were then used to demonstrate the effects of Lake Winnebago 

being the most downstream lake of a chain of lakes by 

examining changes in its response to a 75-percent reduction 

in external P loading (scenario 3–J) but with two changes. 

Scenario 17–J simulated the positive consequences to Lake 

Winnebago from P reductions applied only to the upstream 

lakes (upstream from the Fox River at Oshkosh) with no 

reductions in P loading from the area immediately around 

Lake Winnebago or from the point sources or septic systems 

effluent entering Lake Winnebago. Scenario 18–J simulated 

the negative consequences of Lake Winnebago being downstream from other lakes and simulated the delayed response 

to P reductions that were upstream in the watershed. This was 

done by showing the decrease in transient TP concentrations 

in Lake Winnebago when the TP concentrations leaving the 

Upper Pool Lakes were immediately set to the concentrations 

simulated 125 years after a 75-percent reduction in export 

from their watersheds (using output from scenario 3–J for the 

Upper Pool Lakes).

Algorithms, Data Requirements, and Calibration

The Jensen model (Jensen and others, 2006) (eq. 7) 

describes changes in in-lake TP concentrations caused by daily 

external P loading and water temperature, given the initial 

recyclable P accumulated in the sediments of the lake (PSed), 

by combining its estimations of P release from the sediments 

(eq. 8) and P sedimentation (eq. 9).

Six types of data are required as input into Jensen models: 

morphometric data (volume and mean depth from table 1), the 

initial recyclable (available) P accumulated in the sediments of 

the lake (PSed), daily water temperatures in the lake, daily flows 

into the lake, daily P loading to the lake, and TP concentration 

data from the lake to calibrate the models. All input data used in 

the Jensen models and results from the models are available at 

https://doi.org/10.5066/P9Y8BE4H (Robertson and Kennedy, 

2018). 

For comparison with results from model calibrations, the 

recyclable P accumulated in the sediment of Lake Winnebago 

was also estimated from information collected by Gustin 

(1995). Gustin (1995) estimated that the average depth of the 

zone of active TP recycling in Lake Winnebago was 0.3 m; 

therefore, the volume of active sediment was 0.3 cubic meter 

per square meter of bottom sediment. If the bulk density of 

wet lake sediment is assumed to be 100,000–200,000 grams 

of sediment per cubic meter, then the mass of active sediment 

is 30,000–60,000 grams of sediment per square meter. Gustin 

(1995) also estimated that the average recyclable P content at 

the sediment surface was 17.6 micromoles per gram of sediment 

(or 0.00054 gram of P per gram of sediment). If it is assumed 

that there was no recyclable P at 0.3 m and there was a linear 

decline in recyclable P from the surface to 0.3 m, then the average recyclable P was 0.00027 gram of P per gram of sediment. 

Therefore, the total recyclable P accumulated in the sediment 

should be about 8 to 16 grams per square meter (g/m2).
Table 13. Linked Jensen model simulation results. Phosphorus load changes to the Winnebago Pool Lakes, Wisconsin, and the 

resulting geometric mean total phosphorus concentrations, for the period June 1 through September 14, are given for 125 years 

after the changes in phosphorus loading from the linked Jensen model. Calibrations were conducted from October 1, 2008 through 

September 30, 2013.

[kg, kilogram; conc., concentration; mg/L, milligram per liter. Base conditions for all comparisons are in bold font.]

Scenarios Scenario

Upper Pool Lakes Lake Winnebago

5-year 

average annual 

phosphous load

(kg)

 Total 

phosphorus 

concentration 

(mg/L)

5-year 

average annual 

phosphorus load

(kg)

 Total 

phosphorus 

concentration 

(mg/L)

Calibration

SWAT extrapolations Calibration 305,600 0.117 333,100 0.100

SWAT extrapolations Full linked model 305,600 0.117 347,700 0.101

General response corresponding to percentage change in P load

–80 percent 2–J 61,500 0.024 86,300 0.029

–75 percent 3–J 76,000 0.030 103,000 0.034

–70 percent 4–J 90,400 0.036 119,000 0.038

–69 percent 5–J 93,300 0.037 122,000 0.039

–65 percent 6–J 105,000 0.041 135,000 0.043

–50 percent 7–J 148,000 0.059 184,000 0.058

–25 percent 8–J 220,000 0.087 266,000 0.083

–10 percent 9–J 264,000 0.104 315,000 0.098

0 percent–Base 1–J 293,000 0.116 348,000 0.108

+10 percent 10–J 322,000 0.127 380,000 0.117

+25 percent 11–J 365,000 0.144 429,000 0.133

+50 percent 12–J 437,000 0.173 511,000 0.157

+75 percent 13–J 509,000 0.201 593,000 0.182

+ 100 percent 14–J 581,000 0.230 674,000 0.206

Specific natural and anthropogenic scenarios

Reference conditions 15–J 81,300 0.027 103,000 0.033

Reference plus 9 percent of the 

anthropogenic-affected sources

16–J 100,000 0.035 125,000 0.040

75-percent reduction to only 

phosphorus sources upstream 

of the Fox River at Oshkosh

17–J 76,000 0.030 133,000 0.043

Immediate upstream effects of a 

75-percent reduction in phosphous sources to the Upper Pool 

Lakes

18–J 76,000 0.030 103,000 0.033

44 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 45

Continuous daily water temperatures in the lakes were 

estimated from air temperatures measured at the National 

Weather Service station at Oshkosh, Wis. Water temperatures 

were estimated using the average air temperature during the 

previous 5 days, with days having an estimated 5-day average 

air temperature less than 1 °C set to 1 °C. This resulted in a 

root mean square error (RMSE) between measured and estimated water temperatures of 2.56 °C based on water temperature data measured in Lake Winnebago from 1990 to 2013.

To calibrate the Jensen model, PSed and four additional 

coefficients need to be estimated: sediment release constant 

(bR), temperature-dependence factor for P release (tR), sedimentation constant (bS), and temperature-dependence factor 

for sedimentation (tS). Equations 7–9 were incorporated into 

Excel with daily flow, P loading, and water temperatures as 

inputs to the equations. “Optimal” values for the four coefficients and an initial PSed were obtained using the Solver routine 

in Excel, which was set up to minimize the sum of square 

errors between the daily measured and estimated TP concentrations in the lake. Solver adjusts the values in the decision 

variable cells (four coefficients and initial PSed) to minimize 

the value in an objective cell (sum of square errors between 

measured and estimated in-lake TP concentrations) using a 

Generalized Reduced Gradient Nonlinear method (FrontlineSolvers, 2017).

Because detailed in-lake data were only available for 

May through September for the Upper Pool Lakes and TP data 

are needed throughout the year, Jensen models could not be 

developed for each Upper Pool Lake. Instead, two independent 

Jensen models were initially constructed: one for all the Upper 

Pool Lakes using monthly TP data collected at their outlet 

(Fox River at Oshkosh) as its in-lake TP and one for Lake 

Winnebago using monthly or more frequent TP data collected 

in either the lake or its outlet (Fox River at Neenah Menasha) 

as its in-lake TP.

To calibrate the Jensen model for Lake Winnebago, 

Solver was used to find optimal values for the four coefficients 

and the initial PSed (table 14) for October 1, 2008, through 

December 31, 2013 (about 5 years of data) using flows and 

TP loads measured at the Fox River at Oshkosh and Fond du 

Lac River sites. The unmonitored flows and loads to Lake 

Winnebago were estimated from the Fond du Lac River site 

using SWAT-flow and SWAT-load ratios (1.399 [table 7] and 

0.296, respectively). The 0.296 value was based on the SWAT 

estimated nonpoint P load for the nearshore area (6,140 kg; 

table 7) divided by the total load for the Fond du Lac River 

(20,700 kg; table 8). During calibration, PSed was estimated to 

be 15.0 g/m2, which was within the range estimated from data 

collected by Gustin (1995). This value also kept PSed relatively 

stable throughout the 5-year calibration period. The RMSE 

of the calibrated independent Winnebago Jensen model was 

0.043 mg/L based on 160 measurements.

After the Lake Winnebago Jensen model was calibrated, 

the model was used to simulate the daily P released from the 

sediments and daily P sedimentation from the water column 

(fig. 13A). The difference in these two rates represents the net 

internal P loading into the water column (fig. 13B) and should 

incorporate the effects of diffusion, wind resuspension, and 

other biological effects. During May through September of 

2009–13, the average net P release from the sediments with 

the Jensen model was estimated to be 3.5 mg/m2/d, which was 

a little higher than the 3.0 mg/m2/d estimated using the massbalance approach and 2.8 mg/m2

/d from BATHTUB. There 

was a net deposition of P into the sediments from September 

to April. The average net P release from the sediments for the 

entire year was 0.6 mg/m2/d, which indicates that there should 

be a small net release of P into Lake Winnebago over the 

entire year.

Table 14. Parameters and coefficients used in the calibrated Jensen models for Lake Winnebago and the three Upper Pool 

Lakes. 

Parameter Description Parameter Lake Winnebago Upper Pool Lakes

Volume, in millions of cubic meters Vol 2,415 189.1

Mean depth, in meters z 4.54 1.68

Initial sediment phosphorus content, grams per square meter PSed 15.00 15.00

Sediment release constant bR 0.0004 0.0005

Temperature dependence of phosphorus release t

R 0.3209 0.1175

Sedimentation constant bS 0.0523 0.0523

Temperature dependence of sedimentation t

S 0.0606 0.0639

Summary statistic, sum of square errors SSE 0.2895 0.0424

Summary statistic, root mean sum of square errors RMSE 0.0425 0.0266
46 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

IP-094896-fig13

Date

July 2008 July 2009 July 2010 July 2011 July 2012 July 2013

Net phosphorus loading, in milligrams per square meter per day

0

10

20

30

40

50

-10

B

Phosphorus release and sedimentation, 

in milligrams per square meters per day

0

10

20

30

40

50

60

A

Sediment phosphorus release

Phosphorus sedimentation

EXPLANATION

Net phosphorus sedimentation

EXPLANATION

Figure 13. Phosphorus release, sedimentation, and net internal phosphorus loading for Lake Winnebago, Wisconsin, water 

years 2009–13, on the basis of Lake Winnebago Jensen model results. A, Phosphorus release and sedimentation. B, Net 

phosphorus sedimentation.
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 47

Solver was then used to calibrate the Jensen model for 

the combined three Upper Pool Lakes, for October 1, 2008, 

through December 31, 2013, using daily total flows and P 

loads estimated from measured flows and computed loads 

at the Wolf River at New London and Fox River at Berlin 

extrapolated to the entire basin using SWAT flow and load 

ratios (SWAT-flow ratios of 1.700 and 1.141 for the Wolf and 

Fox Rivers, respectively, and SWAT-load ratios of 1.642 and 

1.124 for the Wolf and Fox Rivers, respectively, table 7). During initial calibration, the minimization process determined a 

sedimentation rate equal to 0, which is unrealistic; therefore, 

the sedimentation rate was set to a value similar to that set for 

Lake Winnebago, and then optimal values for all other coefficients were determined (table 14). During calibration, PSed was 

again estimated to be 15.0 g/m2. This value kept PSed relatively 

stable throughout the 5-year calibration period. The measured 

and simulated TP concentrations for the Upper Pool Jensen 

model are compared in figure 14A. The RMSE of the final 

calibrated model for the Upper Pool Lakes was 0.027 mg/L 

based on 60 measurements.

Output from the calibrated Upper Pool Lakes Jensen 

model was then used as input to the calibrated Winnebago 

model to create one linked Jensen model, which used measured loads at the Wolf River at New London and Fox River 

at Berlin extrapolated to the entire Upper Pool Basin using 

SWAT-flow and SWAT-load ratios and direct flow and P loading to Lake Winnebago based on Fond du Lac River flows 

and P loads. Measured and simulated TP concentrations for 

Lake Winnebago from the linked Jensen model are compared in figure 14B. The RMSE for the measured compared 

to simulated TP concentrations in Lake Winnebago from the 

linked Jenson model was 0.043 mg/L, which is the same as the 

independently calibrated Lake Winnebago Jensen model. The 

measured and simulated annual geometric-mean TP concentrations for June 1 through September 15 (the period for which 

TP criterion for the lake were derived [Wisconsin Department 

of Natural Resources, 2017a]) only for days with coinciding 

data for the linked model are compared in figure 14C. The 

RMSE of the final linked model for annual estimated TP concentrations was 0.018 mg/L based on 5 years of data. These 

model results provided reasonable fit to the measured data, 

thus suggesting the models should provide accurate responses 

to changes in P loading.

Response in Water Quality to Basinwide 

Changes in Phosphorus Loading

In total, 14 scenarios (J–1 through J–14) were simulated 

with the linked Jenson model to estimate the expected 

response in the geometric-mean summer TP (June 1 through 

September 15) in the Upper Pool Lakes and Lake Winnebago 

to changes in controllable P sources and to determine the 

P load reduction required to reach the 0.040 mg/L TP criterion 

for the lakes For all simulations, the Jensen model was first 

used to simulate daily TP concentrations in the lakes during 

WY2009–13 using P loading from the watershed similar to 

that used in the calibration period, except the flows and TP 

loading from the watershed were replaced with flows and loadings fully estimated with SWAT (The Cadmus Group, 2018). 

Then the P inputs for those 5 years were modified based on 

the changes in loading being simulated (such as a 25-percent 

increase in loading simulated as a 25-percent increase in TP 

concentrations) for WY2014–18. These changes were applied 

to all P sources, except inputs from groundwater and the 

precipitation. Then the inputs for 2014 to 2018 were repeated 

over and over in 5-year replicates until 2145. Because the Jensen model simulates transient changes in lake TP after changes 

in P inputs, the expected future in-lake TP concentrations 

depends on the number of years after the change in P loading 

that is evaluated. The simulated changes in geometric-mean 

TP concentrations for the Upper Pool Lakes and Lake Winnebago after a 75-percent reduction in external P loading are 

shown in figure 15. After about 60 years, the recyclable P 

accumulated in the sediments and the in-lake TP in the Upper 

Pool Lakes approach a new equilibrium of about 4 g/m2 and 

0.030 mg/L, respectively; however, the recyclable P accumulated in the sediments and the in-lake TP in Lake Winnebago 

took much longer, over 100 years, to approach a new equilibrium of about 5 g/m2

 and 0.033 mg/L, respectively. Part of the 

reason for the difference in the responses in these two waterbodies was that the TP concentrations of all inflows to the 

Upper Pool Lakes in these simulations immediately changed 

in 2014; however, TP concentrations in the major inflow to 

Lake Winnebago was more gradual, taking several years to 

come to a new equilibrium because of the gradual transition of 

in-lake TP concentrations in the Upper Pool Lakes. Therefore, 

TP concentrations in Lake Winnebago should respond slower 

to external changes in P loadings from throughout basin than 

the Upper Pool Lakes. To describe this gradual decline in TP 

concentrations in the lakes, the geometric-mean TP concentrations for June 1–September 15 for the 5 years just before 

10, 30, 50, 75, and 125 years after the load reduction are 

examined.

Based on Jensen model simulations, TP in the Upper Pool 

Lakes should have a linear response to changes in P loading, 

with a response that varies depending on the number of years 

after the P load changes (fig. 16A; table 13). The changes in 

in-lake TP concentrations in the Upper Pool Lakes gradually approach a similar percent change to that of the external 

P loading: 10 years after the P load reduction, a 75-percent 

change in external P loading (equating to a 74-percent change 

in total loading) should cause about a 50-percent change in 

TP concentrations, but after about 50 years, a 75-percent 

change in loading should cause about a 72-percent change 

in TP concentrations. The changes in in-lake TP concentrations in Lake Winnebago approach a similar change to that 

of the external P loading, but much more gradually than in 

the Upper Pool Lakes: after 75 years, a 75-percent change in 

external P loading (equating to a reduction in total loading 

of 70 percent) should cause about a 66-percent change in TP 

concentrations.
48 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

IP-094896-fig14

Measured in Lake Winnebago and its Outlet

Model simulated

EXPLANATION

Date

2008 2009 2010 2011 2012 2013

0

0.04

0.08

0.12

0.16

Average total phosphorus concentration, 

in milligrams per liter, June through September

C. Lake Winnebago

0

0.05

0.10

0.15

0.20

0.25

B. Lake Winnebago

Total phosphorus concentration, 

in milligrams per liter

Model simulated

Measured Lake Winnebago and its outlet

Measured in Lake Winnebago

EXPLANATION

Model simulated

Measured at the Fox River at Oshkosh

EXPLANATION

A. Upper Pool Lakes

Total phosphorus concentration, 

in milligrams per liter

0

0.05

0.10

0.15

0.20

0.25

Figure 14. Measured and simulated (with the linked Jensen model) near-surface total phosphorus concentrations 

in the Upper Pool Lakes and Lake Winnebago, Wisconsin, water years 2009–13. A, Upper Pool Lakes. B, Lake Winnebago. 

C, Annual June 1 through September 15 geometric mean total phosphorus concentrations in Lake Winnebago.
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 49

IP-094896-fig 15

Winnebago total phosphorus concentration

All Inflow phosphorus concentration 

Sediment phosphorus content

EXPLANATION

Total phosphorus criterion for Winnebago Pool Lakes

Lake total phosphorus concentration, in milligrams per liter

0

0.03

0.06

0.09

0.12

0.15

Lake Winnebago 

0

2

4

6

8

10

12

14

16

Sediment phosphorus, in grams per square meter

2005 2015 2025 2035 2045 2055 2065 2075 2085 2095 2105 2115 2125 2135 2145

Upper Pool total phosphorus concentration

Inflow phosphorus concentration (May to September)

Sediment phosphorus content

EXPLANATION

Total phosphorus criterion for Winnebago Pool Lakes

0

0.03

0.06

0.09

0.12

0.15

Lake total phosphorus concentration, in milligrams per liter

0

2

4

6

8

10

12

14

16

Sediment phosphorus, in grams per square meter

Upper Pool Lakes

Year

Figure 15. Simulated annual geometric mean total phosphorus concentrations for the Upper Pool Lakes and Lake Winnebago, 

Wisconsin, during water years 2009–2145 after a 75-percent reduction in external phosphorus loading using the linked Jensen 

model.
50 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

4896_fig 16

–100

–50

0

50

100

0.00

0.05

0.10

0.15

0.20

0.25

–75 –50 –25 0 25 50 75 100

Percentage change

A. Upper Pool Lakes

Total phosphorus concentration, in milligrams per liter

B. Lake Winnebago

0.00

0.05

0.10

0.15

0.20

0.25

–100

–100 –75 –50 –25 0 25 50 75 100

Total phosphorus concentration, in milligrams per liter

Percentage change

Change in phosphorus loading, in percent

–100

–50

0

50

100

Change in phosphorus loading, in percent

50 years after change

75 years after change

125 years after change

2009 to 2013 conditions

10 years after change

30 years after change

Phosphorus criterion

EXPLANATION

75-percent

reduction in

upstream

sources

Reference

conditions

Reference

plus 

9 percent

Immediate

upstream effects 

of 75-percent 

reduction

75-percent

reduction in

upstream

sources

Reference

conditions

Reference

plus 

9 percent

Immediate

upstream effects 

of 75-percent 

reduction

Figure 16. Simulated changes in the total phosphorus concentrations for the Upper Pool Lakes and 

Lake Winnebago, Wisconsin, in response to various phosphorus-loading scenarios (table 13) using the linked 

Jensen model. Response in the 5-year June 1 through September 15 geometric mean total phosphorus 

concentrations for A, the Upper Pool Lakes and B, Lake Winnebago.
Importance of Internal Phosphorus Loading 51

Based on the response curves for the Upper Pool Lakes 

(fig. 16A), it would require about a 65-percent reduction in 

external P loading and about 125 years or a 75-percent reduction in external P loading and about 30 years for the Upper 

Pool Lakes to reach a geometric-mean June 1–September 15 

TP concentration of 0.040 mg/L (the P criterion for these 

lakes). Based on the response curves for Lake Winnebago, 

a 75-percent reduction in P loading and 75 years are needed 

for the lake to reach a geometric-mean June 1–September 15 

TP concentration of 0.040 mg/L or a 69-percent reduction in 

P loading and about 100 years. These reductions in P loading 

to reach the TP criterion are close to the 73-percent reduction 

estimated with BATHTUB.

Potential Water Quality

To determine the best potentially achievable WQ in 

the lakes (that is, reference conditions), TP concentrations 

in all tributaries to the lakes were again set to 0.020 mg/L, 

and P inputs from point sources and septic systems were 

eliminated (scenario 15–J, which is similar to scenario 16 

with BATHTUB). Based on results from the linked Jensen 

model (fig. 16; table 13), the lowest possible geometric mean 

TP should be 0.027 mg/L for the Upper Pool Lakes and 

0.033 mg/L for Lake Winnebago. These TP concentrations are 

better than the TP criterion for shallow drainage lakes in Wisconsin (Wisconsin Department of Natural Resources, 2017a).

Effects of Specific Phosphorus Reductions 

in the Watershed

To determine how much anthropogenic P inputs could 

be added to reference P loading and yet maintain a 5-year 

geometric-mean summer TP concentration at or below 

0.040 mg/L, all the anthropogenic sources were systematically 

adjusted. If all TP concentrations in the streams, point sources, 

and septic systems increase less than 9 percent from their 

reference concentrations (scenario 16–J, which is similar to 

scenario 17 with BATHTUB), the geometric-mean TP concentration in the Upper Pool Lakes and Lake Winnebago in 

125 years should both stay at or below 0.040 mg/L, which is 

similar to that determined using BATHTUB. However, Jensen 

model results demonstrate how long it will take to reach this 

concentration.

Quite similar reductions in external P loading required for 

TP in Lake Winnebago to reach 0.040 mg/L were determined 

using the Jensen and BATHTUB models even though each 

model used different inputs: the Jensen model used P loading 

for all 12 months, whereas the BATHTUB model used 

P loading only for May through September.

Importance of Internal Phosphorus 

Loading

Changes in external P loading drives changes in-lake 

TP (fig. 9) and productivity, and then the P is either exported 

out the outlet (in drainage lakes) or deposited in the bottom 

sediments. Not all P deposited in the sediments remains there 

because some is released back into the water column from 

internal P loading. Typically, P is released from the sediments 

by diffusion, which typically increases substantially when 

oxygen is completely depleted (anoxia) near or in the bottom 

sediment (Mortimer, 1941). The amount of P released from 

diffusion was quantified by incubating sediment cores from 

the Pool Lakes and measuring DO conditions in the lakes (in 

great detail in Lake Winnebago). Because of extensive mixing, anaerobic conditions were seldom, if ever, measured in 

routine monitoring or with continuous recording instruments 

deployed below a buoy in Lake Winnebago (fig. 2); therefore, 

the aerobic P release rates were used to estimate P released 

from diffusion. The amount of P released from the sediments 

on the basis of laboratory-estimated rates, however, was not 

sufficient to describe the changes in TP observed in the lakes 

using the phosphorus mass-balance approach (fig. 9). In addition to simple diffusion, sediment resuspension caused by 

strong winds can increase sediment P release in shallow lakes 

(Søndergaard and others, 1992; Cyr and others, 2009; Lin 

and Wu, 2013; Huang and others, 2016), and aquatic animals 

can increase internal P loading in lakes through their feeding 

behavior (stirring up the sediments) and excretion (Lamarra, 

1975; Andersson and others, 1988; Fischer and others, 2013). 

These processes may increase the internal P released in 

the Winnebago Pool Lakes. Results from the mass-balance 

approach (fig. 9), the BATHTUB model, and the Jensen 

models all indicate that the net internal P release rate for 

May–September was about 2.8–3.5 mg/m2/d, which is about 

7 to 8 times more than laboratory rates for diffusion from 

aerobic sediments and about twice the rate estimated for diffusion from anaerobic sediments. Therefore, internal P release 

in these lakes seems to be much higher than that estimated 

directly from the sediment core studies. These release rates 

are similar to those estimated in other large shallow eutrophic 

lakes (for example, 5.56 mg/m2/d in Lake Taihu, China; Huang 

and others, 2016).

Relatively similar internal P loading to Lake Winnebago 

was estimated using three different approaches (mass-balance 

approach, the BATHTUB model, and the Jensen model); 

however, all three of the approaches were based on similar 

external P loading rates to the lake. Therefore, similar internal 

P loading may have been expected. Part of the P estimated to 

be from internal loading may be a result of errors in the other 

components of the P budgets; however, given that most of 

the P load to Lake Winnebago was from monitored tributary 

loading (Fox River and Fond du Lac River) and input from 

precipitation, this estimate of P from internal loading should 

be considered quite reliable.
52 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

Because of the P being released from processes in 

addition to diffusion, net internal P loading is an important 

source of P to each of the lakes, but it did vary in its relative 

importance among lakes because of the magnitude of the 

other sources and the varying residence time among lakes. 

On the basis of the net internal P loading rates estimated with 

BATHTUB, the importance of net internal P loading during 

May–September varied from about 3 percent for Lake Winneconne, to about 14 percent for Lake Poygan and Lake Butte 

des Morts, and to 55 percent for Lake Winnebago (table 9). 

Although most of the external P inputs to Lake Winnebago 

could be accurately estimated, more assumptions were needed 

to estimate the total external P inputs to the other Upper Pool 

Lakes; therefore, their estimated internal P loading should be 

considered less reliable than those for Lake Winnebago.

The internal P loading from the sediments during summer 

not only increases in-lake TP concentrations throughout summer, but it also results in an increase in Chl-a and a decrease 

in water clarity (SD) as summer progresses (fig. 3). These 

changes in WQ result in all the Winnebago Pool Lakes being 

classified as hypereutrophic by late summer.

Although the net internal P loading rate was relatively 

high in all Winnebago Pool Lakes during summer, results from 

the Jensen model indicate that there is a net P deposition back 

to the sediments during the rest of the year (fig. 13), which 

results in the sediments having little net effect on the annual 

P budget of Lake Winnebago. Based on the mass-balance 

approach, there was a slight accumulation of P in the lake 

(table 8), and based on the Jensen model there was a slight net 

release of P from the sediments (about 0.6 mg/m2/d).

Lakes with high internal P loading may respond much 

slower to reductions in external P loading than lakes with 

relatively low internal P loading (Jeppesen and others, 2005, 

Jensen and others, 2006, Meals and others, 2010). Even 

20 years after external P load reductions to Shagawa Lake, 

Minn., internal P loading continued to affect its trophic state 

(Seo and Canale, 1999). Results from the Jensen models demonstrate how P from internal loading can delay the full effects 

of external P load reductions from being achieved (figs. 15 and 

16). Although changes in external P loading were simulated 

to happen immediately in all the Jensen simulations, it took 

several decades for the sediment P content (fig. 15) and its 

associated P release to reach equilibrium. About 10–15 years 

after the external P load reduction of 75 percent, the geometric 

mean for the May–September period for the Upper Pool Lakes 

should decrease from about 0.115 to about 0.050 mg/L, and 

the geometric mean for Lake Winnebago should decrease from 

about 0.101 to about 0.073 mg/L. TP concentrations reached 

equilibrium in the Upper Pool Lakes (0.031 mg/L) in about 

50 to 60 years, but TP concentrations in Lake Winnebago 

reached its new equilibrium (0.033 mg/L) in about 100 years.

Effects of Changes in Phosphorus 

Loading Cascading Down a Chain of 

Lakes

Lakes typically are considered to be singular entities in 

the environment (Forbes, 1887) and, therefore, typically are 

modeled as such. However, in a chain of lakes, such as the Winnebago Pool, effects of changes upstream in the watershed affect 

the lakes downstream (Lathrop and Carpenter, 2014; Carpenter 

and Lathrop, 2014). The location of Lake Winnebago being 

at the downstream end of a chain of lakes can have beneficial 

and detrimental effects. Being downstream from other lakes, it 

should benefit from any actions done to improve the WQ of the 

upstream lakes; however, there should be a delayed response 

to changes made in the watershed, especially in lakes where 

internal P loading is important to its P budget (Jeppesen and 

others, 2005, Meals and others, 2010; Jensen and others, 2006). 

To examine the beneficial and detrimental effects caused by 

Lake Winnebago being the downstream member in a chain of 

lakes, two additional scenarios were simulated with the linked 

Jensen model (scenarios 17–J and 18–J). In figure 17, the 5-year 

moving-average geometric-mean summer TP concentrations are 

plotted for a 75-percent reduction in external loading throughout 

the entire watershed (scenario 3–J). Scenario 17–J simulates the 

effects of a 75-percent reduction only applied to the watersheds 

of the three upstream lakes, with no changes in external P loading directly around Lake Winnebago. Results of this simulation 

show that there is still a large decrease in TP in Lake Winnebago, 

from 0.116 to 0.048 mg/L (computed for the May–September 

period). Thus, there is a beneficial effect of being downstream 

in a chain of lakes. Actions improving the WQ of any upstream 

lake will also have beneficial effects to the downstream lakes.

The Upper Pool Lakes, however, also delay the effects of 

actions done throughout the watershed of a downstream lake, 

which can be seen in scenario 18–J. This scenario simulates 

what would happen if the full effects of a 75-percent reduction 

in P inputs are immediately input into Lake Winnebago. TP 

concentrations decline more quickly but ultimately reach the 

same TP concentration after about 100 years. After a 75-percent 

reduction, it should take about 25 years for 50 percent of the 

effects to be observed in Lake Winnebago; however, if the reduction in external loading was done immediately, it should only 

take about 20 years for 50 percent of the effects to be observed. 

The largest detrimental lag effect is seen about 15 years after 

the 75-percent reduction in P inputs, when TP concentrations in 

Lake Winnebago would have been about 0.007 mg/L lower if 

the Upper Pool Lakes did not delay the effects of the external 

P reductions. The delay in the changes in TP concentrations in 

Lake Winnebago primarily is because much of P loading to Lake 

Winnebago comes from the Upper Pool Lakes whose TP concentrations take several years to reach equilibrium. Therefore, 

the delayed reduction in P loadings to Lake Winnebago from 

the upstream lakes delays the changes in its sediment P content, 

which further delays the changes in its TP concentration.
Summary and Conclusions 53

IP-094896-fig17

Scenario 3−J: Base with 75-percent phosphorus load reduction

Scenario 17−J: No downstream phosphorus reductions

Scenario 18−J: Immediate upstream effects

EXPLANATION

Changes in total phosphorus concentrations in Lake Winnebago

Total phosphorus concentration, in millligrams per liter

0

0.03

0.06

0.09

0.12

2005 2025 2045 2065 2085 2105 2125 2145

Year

Figure 17. Simulated changes in the total phosphorus concentrations in Lake Winnebago, Wisconsin, in response 

to various phosphorus-loading scenarios using the linked Jensen model, demonstrating beneficial and detrimental 

effects of it being in a chain of lakes.

Summary and Conclusions

The Winnebago Pool is a chain of four shallow lakes 

that has received extensive phosphorus (P) inputs from its 

agricultural watershed during the past 150 years. These inputs 

have resulted in increased in-lake total phosphorus (TP) 

concentrations in all four lakes and much P trapped in their 

sediments. Because the in-lake TP concentrations exceed their 

TP criterion, all four Pool Lakes are now included on Wisconsin’s impaired waters list. This study was done to determine 

how changes in P inputs to the lakes should affect their water 

quality (WQ) and how being a member of a chain of lakes 

affects this response. Further, the study determined the reduction in P loading needed for each lake to attain their 

TP criterion.

As part of the study, detailed WQ data were collected 

in the four lakes during 2009–11 to document their current 

WQ. During May–September of these years, all four lakes had 

extensive periodic vertical mixing resulting in relatively uniform WQ throughout the water column in each lake. Average 

TP concentrations for June–September ranged from 0.088 milligram per liter (mg/L) in Lake Winneconne to 0.104 mg/L in 

Lake Butte des Morts, average Chlorophyll-a (Chl-a) concentrations ranged from 30.5 micrograms per liter (μg/L) in 

Lake Winnebago to 52.1 μg/L in Lake Butte des Morts, and 

average Secchi depths (SDs) ranged from 0.54 meter (m) in 

Lake Butte des Morts to 1.15 m in Lake Winnebago. TP and 

Chl-a concentrations increased and SDs decreased as summer 

progressed, resulting in each of the lakes becoming hypereutrophic by late summer.

Phosphorus budgets were constructed for each lake. 

External P input from the watershed was the most important source of P to the most upstream lake (Lake Poygan) 

but became less important to downstream lakes as input 

from the adjacent upstream lake became more important: 

for Lake Poygan direct external P loading represented more 

than 96 percent of its total annual P input, compared to about 

8 percent for Lake Winnebago, which had about 80 percent 

of its P input from the adjacent upstream Pool Lake (Lake 

Butte des Morts). The rates of net internal P loading during 

May–September (based on results from the BATHTUB model) 

varied among lakes from 1.2 milligrams per square meter per 

day (mg/m2/d) in Lake Winneconne, to 2.3 mg/m2/d in Lake 

Poygan, to 2.8 mg/m2/d in Lake Winnebago, and to 5.0 mg/

m2/d in Lake Butte des Morts. Similar net internal P load rates 

for Lake Winnebago were determined with a mass-balance 

approach and the Jensen model. These internal P loading 

rates were much higher than what could be explained from 
54 Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin

P diffusion rates estimated from sediment cores incubated 

in the laboratory. The high internal P loading rates in these 

large shallow lakes are believed to be caused by sediment 

resuspension from wind and fish and by biological excretion. 

Based on the internal P loading rates from BATHTUB for 

May–September, the importance of the net internal P loading 

to their summer P budget varied from about 3 percent for Lake 

Winneconne, to about 14 percent for Lake Poygan and Lake 

Butte des Morts, and to 55 percent for Lake Winnebago. Part 

of the P from internal loading may be a result of errors in the 

other components of their P budgets; however, given that most 

of the P load to Lake Winnebago is from monitored tributary loading and precipitation, its estimate of P from internal 

loading should be quite reliable. However, more assumptions 

were needed to estimate the total external P inputs to the other 

Upper Pool Lakes; therefore, their estimated internal P loading 

may be less reliable than that for Lake Winnebago.

To determine how the WQ of the Pool Lakes should 

respond to changes in P loading, and ultimately the magnitude 

of actions that are needed to improve their WQ sufficiently 

such that they can be removed from Wisconsin impaired 

waters list, two eutrophication models (BATHTUB and Jensen 

models) were used to simulate the long-term and transient 

effects of various P-reduction strategies. Results from both 

models indicate that TP, Chl-a, and SD directly respond to 

changes in external P input; and that the P loading into the 

three Upper Pool Lakes (Lakes Poygan, Lake Winneconne, 

and Lake Butte des Morts) needs to be reduced by about 

60 percent and into Lake Winnebago needs to be reduced by 

about 69–73 percent for their mean summer TP concentrations 

to decrease to less than their 0.040 mg/L criterion. Results of 

both models with TP concentrations in all tributaries set to 

0.020 mg/L (reference TP concentration for streams in central 

Wisconsin), and P inputs from point sources and septic systems eliminated, indicate that the best possible mean summer 

WQ is as follows: TP concentrations ranging from 0.022 to 

0.027 mg/L in the Upper Pool Lakes to 0.032–0.033 mg/L in 

Lake Winnebago; Chl-a concentrations ranging from 10 μg/L 

in Lake Poygan, to 14 μg/L in Lakes Winneconne and Winnebago, and to 19 μg/L in Lake Butte des Morts; and SDs 

ranging from 1 m in Lake Butte des Morts, to 1.2 m in Lake 

Poygan and Lake Winneconne, and to 2.2 m in Lake Winnebago. All these values are below the Wisconsin Department 

of Natural Resources WQ criteria for shallow drainage lakes.

BATHTUB was then used to examine the effects of 

reducing internal P loading by an additional 25 percent in each 

of the scenarios to simulate what may happen if in-lake actions 

also are done, such as activities to promote macrophyte growth 

that should reduce wind resuspension or activities to reduce 

the population of rough fish, such as carp, that stir the bottom during feeding and have high excretion rates. If internal 

P loading was reduced an additional 25 percent, the overall 

external P load reduction needed for the all four Pool Lakes to 

reach 0.040 mg/L decreased from a 73-percent reduction in all 

controllable P sources to a 67-percent reduction.

Input of P from internal loading not only increases the 

TP concentrations in the lakes as summer progresses, but it 

also increases Chl-a concentrations, reduces water clarity 

(SD), and should delay the timeframe for the lakes to experience the full effects of external P load reductions. The final 

equilibrium TP concentrations after a 69-percent reduction in 

external P loading to the Upper Pool Lakes (0.037 mg/L) was 

in about 50–60 years, and about 100 years in Lake Winnebago 

(0.039 mg/L).

Changes in WQ resulting from changes in the watershed of a chain of lakes, such as the Winnebago Pool Lakes, 

gradually cascades downstream in the chain. Lake Winnebago 

being the most downstream lake in this chain has beneficial 

and detrimental implications. Because Lake Winnebago is 

downstream from other lakes, results of any action done in the 

watershed of upstream lakes to reduce their P inputs should 

also improve the WQ of all the downstream lakes. However, 

the upstream lakes also delay the response in WQ of the downstream lakes to actions done in the watershed, especially in 

lakes where internal P loading is important to their P budgets.

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Robertson and others—Water-Quality Response to Changes in Phosphorus Loading of the Winnebago Pool Lakes, Wisconsin—Scientific Investigations Report 2018–5099

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20185099